Simplify The Expression:$\[ \frac{48 V^4}{8 V^6} \\]

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it is essential to understand the rules and techniques involved in simplifying expressions. In this article, we will focus on simplifying the given expression $\frac{48 v^4}{8 v^6}$ using various techniques and rules. We will break down the expression into smaller parts, simplify each part, and then combine them to obtain the final simplified expression.

Understanding the Expression

The given expression is a fraction, and it consists of two parts: the numerator and the denominator. The numerator is $48 v^4$, and the denominator is $8 v^6$. To simplify this expression, we need to understand the rules of exponents and fractions.

Rules of Exponents

Exponents are a shorthand way of writing repeated multiplication. For example, $v^4$ means $v \times v \times v \times v$. When we multiply two numbers with the same base, we add their exponents. For example, $v^4 \times v^2 = v^{4+2} = v^6$.

Simplifying the Expression

To simplify the expression $\frac{48 v^4}{8 v^6}$, we can start by simplifying the numerator and the denominator separately. We can factor out the greatest common factor (GCF) from both the numerator and the denominator.

Simplifying the Numerator

The numerator is $48 v^4$. We can factor out the GCF, which is $48$. This gives us $48 \times v^4$. We can simplify this further by dividing $48$ by $8$, which gives us $6$. Therefore, the numerator can be simplified to $6 v^4$.

Simplifying the Denominator

The denominator is $8 v^6$. We can factor out the GCF, which is $8$. This gives us $8 \times v^6$. We can simplify this further by dividing $8$ by $8$, which gives us $1$. Therefore, the denominator can be simplified to $v^6$.

Combining the Simplified Numerator and Denominator

Now that we have simplified the numerator and the denominator, we can combine them to obtain the final simplified expression. We can do this by dividing the numerator by the denominator.

$\frac{6 v^4}{v^6} = 6 v^{4-6} = 6 v^{-2}$

Final Simplified Expression

The final simplified expression is $6 v^{-2}$. This can be rewritten as $\frac{6}{v^2}$.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it is essential to understand the rules and techniques involved in simplifying expressions. In this article, we have focused on simplifying the given expression $\frac{48 v^4}{8 v^6}$ using various techniques and rules. We have broken down the expression into smaller parts, simplified each part, and then combined them to obtain the final simplified expression. The final simplified expression is $\frac{6}{v^2}$.

Additional Tips and Tricks

• When simplifying expressions, it is essential to understand the rules of exponents and fractions.
• Factor out the greatest common factor (GCF) from both the numerator and the denominator.
• Simplify the numerator and the denominator separately before combining them.
• Use the rules of exponents to simplify the expression.
• Rewrite the final simplified expression in a more simplified form.

Frequently Asked Questions

• Q: What is the final simplified expression? A: The final simplified expression is $\frac{6}{v^2}$.
• Q: How do I simplify the expression $\frac{48 v^4}{8 v^6}$? A: To simplify the expression, factor out the greatest common factor (GCF) from both the numerator and the denominator, simplify the numerator and the denominator separately, and then combine them.
• Q: What are the rules of exponents? A: The rules of exponents state that when we multiply two numbers with the same base, we add their exponents.

References

• [1] Algebraic Expressions, Khan Academy
• [2] Simplifying Expressions, Mathway
• [3] Rules of Exponents, Purplemath
  

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Introduction

In our previous article, we simplified the expression $\frac{48 v^4}{8 v^6}$ using various techniques and rules. In this article, we will provide a Q&A section to help you understand the concepts and techniques involved in simplifying expressions.

Q&A

Q: What is the final simplified expression?

A: The final simplified expression is $\frac{6}{v^2}$.

Q: How do I simplify the expression $\frac{48 v^4}{8 v^6}$?

A: To simplify the expression, factor out the greatest common factor (GCF) from both the numerator and the denominator, simplify the numerator and the denominator separately, and then combine them.

Q: What are the rules of exponents?

A: The rules of exponents state that when we multiply two numbers with the same base, we add their exponents. For example, $v^4 \times v^2 = v^{4+2} = v^6$.

Q: How do I factor out the greatest common factor (GCF) from both the numerator and the denominator?

A: To factor out the GCF, identify the largest number that divides both the numerator and the denominator. Then, divide both the numerator and the denominator by this number.

Q: What is the greatest common factor (GCF) of 48 and 8?

A: The greatest common factor (GCF) of 48 and 8 is 8.

Q: How do I simplify the numerator and the denominator separately?

A: To simplify the numerator and the denominator separately, divide each number by the greatest common factor (GCF).

Q: How do I combine the simplified numerator and denominator?

A: To combine the simplified numerator and denominator, divide the numerator by the denominator.

Q: What is the final simplified expression?

A: The final simplified expression is $\frac{6}{v^2}$.

Q: Can I simplify expressions with variables?

A: Yes, you can simplify expressions with variables using the same techniques and rules as you would with numerical expressions.

Q: How do I simplify expressions with negative exponents?

A: To simplify expressions with negative exponents, rewrite the expression with a positive exponent by moving the base to the other side of the fraction.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not factoring out the greatest common factor (GCF) from both the numerator and the denominator.
• Not simplifying the numerator and the denominator separately.
• Not combining the simplified numerator and denominator correctly.
• Not using the rules of exponents correctly.

Conclusion

Simplifying expressions is an essential skill in mathematics, and it is crucial to understand the rules and techniques involved in simplifying expressions. In this article, we have provided a Q&A section to help you understand the concepts and techniques involved in simplifying expressions. We hope this article has been helpful in clarifying any doubts you may have had about simplifying expressions.

Additional Tips and Tricks

• Always factor out the greatest common factor (GCF) from both the numerator and the denominator.
• Simplify the numerator and the denominator separately before combining them.
• Use the rules of exponents to simplify the expression.
• Rewrite the final simplified expression in a more simplified form.
• Practice simplifying expressions with variables and negative exponents.

Frequently Asked Questions

• Q: What is the final simplified expression? A: The final simplified expression is $\frac{6}{v^2}$.
• Q: How do I simplify the expression $\frac{48 v^4}{8 v^6}$? A: To simplify the expression, factor out the greatest common factor (GCF) from both the numerator and the denominator, simplify the numerator and the denominator separately, and then combine them.
• Q: What are the rules of exponents? A: The rules of exponents state that when we multiply two numbers with the same base, we add their exponents.

References

• [1] Algebraic Expressions, Khan Academy
• [2] Simplifying Expressions, Mathway
• [3] Rules of Exponents, Purplemath