Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.1 - Exponents and Scientific Notation - Exercise Set: 148

Answer

$5^{-9}$

Work Step by Step

We are given the numbers $5^{-10}$ and $5^{-9}$. We know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer). Without calculating completely, we know that $5^{-10}=\frac{1}{5^{10}}=\frac{1}{5^{9}\times5^{1}}$. Therefore, both numbers will have the same numerator, but $5^{-10}$ will have a denominator that is $5^{1}=5$ times greater than the denominator of $5^{-9}$. So, we know that $5^{-9}$ will be a larger number.
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