Simplify. Assume All Variables Are Positive.${ W^{\frac{6}{7}} \div W^{\frac{4}{7}} }$Write Your Answer In The Form { A $}$ Or { \frac{A}{B}$}$, Where { A $}$ And { B $}$ Are Constants Or Variable

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems more efficiently. When dealing with exponents, we often encounter expressions like $w^{\frac{6}{7}} \div w^{\frac{4}{7}}$. In this article, we will simplify this expression and provide a step-by-step guide on how to do it.

Understanding Exponents

Before we dive into simplifying the expression, let's quickly review what exponents are. An exponent is a small number that is written to the upper right of a number or a variable. It tells us how many times to multiply the number or variable by itself. For example, $w^3$ means $w$ multiplied by itself three times, or $w \times w \times w$.

Simplifying the Expression

Now that we have a basic understanding of exponents, let's simplify the expression $w^{\frac{6}{7}} \div w^{\frac{4}{7}}$. To do this, we can use the quotient rule of exponents, which states that when we divide two powers with the same base, we subtract the exponents.

Step 1: Apply the Quotient Rule

The quotient rule of exponents tells us that when we divide two powers with the same base, we subtract the exponents. In this case, we have:

$$w^{\frac{6}{7}} \div w^{\frac{4}{7}} = w^{\frac{6}{7} - \frac{4}{7}}$$

Step 2: Simplify the Exponent

Now that we have applied the quotient rule, we can simplify the exponent by subtracting the fractions:

$$w^{\frac{6}{7} - \frac{4}{7}} = w^{\frac{2}{7}}$$

Step 3: Write the Final Answer

And that's it! We have simplified the expression $w^{\frac{6}{7}} \div w^{\frac{4}{7}}$ to $w^{\frac{2}{7}}$.

Conclusion

Simplifying expressions with exponents can be a bit tricky, but with the quotient rule and a basic understanding of exponents, we can simplify even the most complex expressions. In this article, we simplified the expression $w^{\frac{6}{7}} \div w^{\frac{4}{7}}$ to $w^{\frac{2}{7}}$. We hope this article has provided you with a better understanding of how to simplify expressions with exponents.

Example Problems

Here are a few example problems to help you practice simplifying expressions with exponents:

• $x^{\frac{3}{4}} \div x^{\frac{2}{4}}$
• $y^{\frac{5}{6}} \div y^{\frac{3}{6}}$
• $z^{\frac{7}{8}} \div z^{\frac{5}{8}}$

Practice Problems

Try simplifying the following expressions:

• $a^{\frac{2}{3}} \div a^{\frac{1}{3}}$
• $b^{\frac{4}{5}} \div b^{\frac{2}{5}}$
• $c^{\frac{6}{9}} \div c^{\frac{3}{9}}$

Answer Key

Here are the answers to the example problems:

• $x^{\frac{3}{4}} \div x^{\frac{2}{4}} = x^{\frac{1}{4}}$
• $y^{\frac{5}{6}} \div y^{\frac{3}{6}} = y^{\frac{2}{6}} = y^{\frac{1}{3}}$
• $z^{\frac{7}{8}} \div z^{\frac{5}{8}} = z^{\frac{2}{8}} = z^{\frac{1}{4}}$

And here are the answers to the practice problems:

• $a^{\frac{2}{3}} \div a^{\frac{1}{3}} = a^{\frac{1}{3}}$
• $b^{\frac{4}{5}} \div b^{\frac{2}{5}} = b^{\frac{2}{5}}$
• $c^{\frac{6}{9}} \div c^{\frac{3}{9}} = c^{\frac{3}{9}} = c^{\frac{1}{3}}$
  Simplify: $w^{\frac{6}{7}} \div w^{\frac{4}{7}}$ Q&A =====================================================

Introduction

In our previous article, we simplified the expression $w^{\frac{6}{7}} \div w^{\frac{4}{7}}$ to $w^{\frac{2}{7}}$. However, we know that there are many more questions and doubts that our readers may have. In this article, we will address some of the most frequently asked questions about simplifying expressions with exponents.

Q&A

Q: What is the quotient rule of exponents?

A: The quotient rule of exponents states that when we divide two powers with the same base, we subtract the exponents. In other words, if we have $a^m \div a^n$, then $a^m \div a^n = a^{m-n}$.

Q: How do I apply the quotient rule of exponents?

A: To apply the quotient rule of exponents, we simply subtract the exponents. For example, if we have $w^{\frac{6}{7}} \div w^{\frac{4}{7}}$, we would subtract the exponents to get $w^{\frac{6}{7} - \frac{4}{7}}$.

Q: What if the exponents are fractions?

A: If the exponents are fractions, we can still apply the quotient rule of exponents. We simply subtract the fractions. For example, if we have $w^{\frac{6}{7}} \div w^{\frac{4}{7}}$, we would subtract the fractions to get $w^{\frac{2}{7}}$.

Q: Can I simplify expressions with exponents that have different bases?

A: Unfortunately, the quotient rule of exponents only applies to expressions with the same base. If we have expressions with different bases, we cannot simplify them using the quotient rule of exponents.

Q: How do I simplify expressions with exponents that have negative exponents?

A: To simplify expressions with exponents that have negative exponents, we can use the rule that $a^{-n} = \frac{1}{a^n}$. For example, if we have $w^{-\frac{3}{4}}$, we can rewrite it as $\frac{1}{w^{\frac{3}{4}}}$.

Q: Can I simplify expressions with exponents that have variables in the exponents?

A: Yes, we can simplify expressions with exponents that have variables in the exponents. We simply apply the quotient rule of exponents as usual. For example, if we have $x^{\frac{2}{3}} \div x^{\frac{1}{3}}$, we would subtract the exponents to get $x^{\frac{1}{3}}$.

Conclusion

Simplifying expressions with exponents can be a bit tricky, but with the quotient rule of exponents and a basic understanding of exponents, we can simplify even the most complex expressions. In this article, we addressed some of the most frequently asked questions about simplifying expressions with exponents. We hope this article has provided you with a better understanding of how to simplify expressions with exponents.

Practice Problems

Try simplifying the following expressions:

• $a^{\frac{2}{3}} \div a^{\frac{1}{3}}$
• $b^{\frac{4}{5}} \div b^{\frac{2}{5}}$
• $c^{\frac{6}{9}} \div c^{\frac{3}{9}}$

Answer Key

Here are the answers to the practice problems:

• $a^{\frac{2}{3}} \div a^{\frac{1}{3}} = a^{\frac{1}{3}}$
• $b^{\frac{4}{5}} \div b^{\frac{2}{5}} = b^{\frac{2}{5}}$
• $c^{\frac{6}{9}} \div c^{\frac{3}{9}} = c^{\frac{3}{9}} = c^{\frac{1}{3}}$

Additional Resources

If you are struggling to simplify expressions with exponents, we recommend checking out the following resources:

• Khan Academy: Exponents and Exponential Functions
• Mathway: Exponents and Exponential Functions
• Wolfram Alpha: Exponents and Exponential Functions

We hope this article has provided you with a better understanding of how to simplify expressions with exponents. If you have any further questions or concerns, please don't hesitate to reach out to us.