Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises: 105

Answer

$\frac{1}{3}$

Work Step by Step

According to the product rule for exponents, $a^{m}\times a^{n}=a^{m+n}$ (where $m$ and $n$ are integers and $a$ is a real number). Therefore, $3^{5}\times 3^{-6}=3^{5+(-6)}=3^{-1}$. According to the definition of negative exponents, $a^{-n}=\frac{1}{a^{n}}$ (where $a\ne0$). Therefore, $3^{-1}=\frac{1}{3^{1}}=\frac{1}{3}$.
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