## Algebra 1

Published by Prentice Hall

# Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Lesson Check - Page 417: 4

#### Answer

$4x^3$

#### Work Step by Step

We want to simplify $\frac{4}{x^{-3}}$ The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. Therefore, we can rewrite the expression as $\frac{4}{\frac{1}{x^3}}$ We can simplify this complex fraction by writing it as a division problem: $\frac{4}{1}\div\frac{1}{x^3}$ To divide fractions, we multiply by the reciprocal: $\frac{4}{1}\times\frac{x^3}{1}$ We multiply to get the answer: $4x^3$

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