Intermediate Algebra (6th Edition)

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

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 17

Answer

8

Work Step by Step

We know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}$ (where m and n are positive integers greater than 1 with $\frac{m}{n}$ in simplest form and $\sqrt[n] a$ is a real number). Therefore, $16^{\frac{3}{4}}=(\sqrt[4] 16)^{3}=2^{3}=8$ We know that $\sqrt[4] 16=2$ because $2^{4}=2\times2\times2\times2=16$
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