Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Concept Quiz 5.6: 7

Answer

True

Work Step by Step

The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$ We use this rule to rewrite the expression $\frac{1}{x^{-2}}$ as $\frac{1}{\frac{1}{x^{2}}}$. We rewrite this fraction as a division problem: $\frac{1}{1}÷\frac{1}{x^2}$ To divide fractions, we multiply by the reciprocal: $\frac{1}{1}\times\frac{x^2}{1}=x^2$ The statement is true.
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