Find The Positive Solution Of The Equation:${ 7x^{\frac{6}{5}} - 12 = 5091 }$

Introduction

In this article, we will delve into the world of mathematics and explore a method to find the positive solution of a given equation. The equation in question is $7x^{\frac{6}{5}} - 12 = 5091$. We will break down the solution process into manageable steps, making it easier to understand and follow along.

Understanding the Equation

The given equation is $7x^{\frac{6}{5}} - 12 = 5091$. To begin solving this equation, we need to isolate the variable $x$. The first step is to add $12$ to both sides of the equation, which gives us:

$$7x^{\frac{6}{5}} = 5103$$

Isolating the Variable

Now that we have isolated the term containing the variable, we can proceed to solve for $x$. To do this, we need to get rid of the coefficient $7$ that is being multiplied by the variable. We can do this by dividing both sides of the equation by $7$, which gives us:

$$x^{\frac{6}{5}} = \frac{5103}{7}$$

Simplifying the Right-Hand Side

The right-hand side of the equation is a fraction, which can be simplified by dividing the numerator and denominator by their greatest common divisor. In this case, the numerator and denominator are both divisible by $3$, so we can simplify the fraction as follows:

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3$$

However, we can simplify it further by dividing the numerator and denominator by their greatest common divisor, which is 3.

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

$$x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 729 \times 3 = 2187/3$$

x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701<br/> **Solving the Equation: A Step-by-Step Guide** =====================================================

Q&A: Frequently Asked Questions

Q: What is the given equation? A: The given equation is $7x^{\frac{6}{5}} - 12 = 5091$.

Q: How do I isolate the variable $x$? A: To isolate the variable $x$, we need to get rid of the coefficient $7$ that is being multiplied by the variable. We can do this by dividing both sides of the equation by $7$, which gives us:

x^{\frac{6}{5}} = \frac{5103}{7} </span></p> <p><strong>Q: How do I simplify the right-hand side of the equation?</strong> A: The right-hand side of the equation is a fraction, which can be simplified by dividing the numerator and denominator by their greatest common divisor. In this case, the numerator and denominator are both divisible by <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn></mrow><annotation encoding="application/x-tex">3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span></span></span></span>, so we can simplify the fraction as follows:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msup><mi>x</mi><mfrac><mn>6</mn><mn>5</mn></mfrac></msup><mo>=</mo><mfrac><mn>5103</mn><mn>7</mn></mfrac><mo>=</mo><mfrac><mn>1701</mn><mrow><mn>7</mn><mi mathvariant="normal">/</mi><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1701</mn><mn>7</mn></mfrac><mo>×</mo><mfrac><mn>3</mn><mn>1</mn></mfrac><mo>=</mo><mn>729</mn><mo>×</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.004em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.004em;"><span style="top:-3.413em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span 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nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1701</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">729</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span></span></span></span></span></p> <p>However, we can simplify it further by dividing the numerator and denominator by their greatest common divisor, which is 3.</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msup><mi>x</mi><mfrac><mn>6</mn><mn>5</mn></mfrac></msup><mo>=</mo><mfrac><mn>5103</mn><mn>7</mn></mfrac><mo>=</mo><mfrac><mn>1701</mn><mrow><mn>7</mn><mi mathvariant="normal">/</mi><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1701</mn><mn>7</mn></mfrac><mo>×</mo><mfrac><mn>3</mn><mn>1</mn></mfrac><mo>=</mo><mn>729</mn><mo>×</mo><mn>3</mn><mo>=</mo><mn>2187</mn><mi mathvariant="normal">/</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">x^{\frac{6}{5}} = \frac{5103}{7} = \frac{1701}{7/3} = \frac{1701}{7} \times \frac{3}{1} = 729 \times 3 = 2187/3 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.004em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.004em;"><span style="top:-3.413em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">5</span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">6</span></span></span></span></span><span class="vlist-s">​</span></span><span 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style="height:3em;"></span><span class="mord"><span class="mord">5103</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2574em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">7/3</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1701</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1701</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">729</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2187/3</span></span></span></span></span></p> <p><strong>Q: How do I solve for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span>?</strong> A: To solve for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span>, we need to get rid of the exponent <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>6</mn><mn>5</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{6}{5}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">5</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">6</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span> that is being applied to the variable. We can do this by raising both sides of the equation to the power of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>5</mn><mn>6</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{5}{6}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">6</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">5</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>, which gives us:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>x</mi><mo>=</mo><msup><mrow><mo fence="true">(</mo><mfrac><mn>2187</mn><mn>3</mn></mfrac><mo fence="true">)</mo></mrow><mfrac><mn>5</mn><mn>6</mn></mfrac></msup></mrow><annotation encoding="application/x-tex">x = \left(\frac{2187}{3}\right)^{\frac{5}{6}} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.744em;vertical-align:-0.95em;"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2187</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.7939em;"><span style="top:-4.2029em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">6</span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">5</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p><strong>Q: What is the value of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span>?</strong> A: To find the value of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span>, we need to evaluate the expression <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mo fence="true">(</mo><mfrac><mn>2187</mn><mn>3</mn></mfrac><mo fence="true">)</mo></mrow><mfrac><mn>5</mn><mn>6</mn></mfrac></msup></mrow><annotation encoding="application/x-tex">\left(\frac{2187}{3}\right)^{\frac{5}{6}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5439em;vertical-align:-0.35em;"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2187</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.1939em;"><span style="top:-3.6029em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">6</span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">5</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span>. This can be done using a calculator or by simplifying the expression further.</p> <p class='katex-block'><span class="katex-error" title="ParseError: KaTeX parse error: Unexpected end of input in a macro argument, expected &#x27;}&#x27; at end of input: …29^{\frac{5}{6 " style="color:#cc0000">x = \left(\frac{2187}{3}\right)^{\frac{5}{6}} = \left(729\right)^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6}} = 729^{\frac{5}{6 </span></p>