Chapter 6 - Radical Functions and Rational Exponents - Chapter Review - Page 424: 37

$25$

RECALL: (1) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ (2) If $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers, then $\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{ab}$. Use the rules above to obtain: \begin{align*} 5^{\frac{3}{2}} \cdot 5^{\frac{1}{2}}&=\sqrt{5^3} \cdot \sqrt{5}\\ &=\sqrt{5^3(5)}\\ &=\sqrt{5^4}\\ &=\sqrt{(5^2)(5^2)}\\ &=5^2\\ &=25 \end{align*}