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: 28

Answer

$\frac{343}{125}$

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, $(\frac{49}{25})^{\frac{3}{2}}=(\sqrt \frac{49}{25})^{3}=(\frac{7}{5})^{3}=\frac{7}{5}\times\frac{7}{5}\times\frac{7}{5}=\frac{7\times7\times7}{5\times5\times5}=\frac{343}{125}$. We know that $\sqrt \frac{49}{25}=\frac{7}{5}$, because $(\frac{7}{5})^{2}=\frac{49}{25}$
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