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: 106

Answer

$\frac{1}{16}$

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, $4^{4}\times 4^{-6}=4^{4+(-6)}=4^{-2}$. According to the definition of negative exponents, $a^{-n}=\frac{1}{a^{n}}$ (where $a\ne0$). Therefore, $4^{-2}=\frac{1}{4^{2}}=\frac{1}{16}$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.