Question

Another question I need help with. I've got the part where it says to rewrite as a radical expression on my paper, but I'm having trouble simplifying.

Answer 1

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------\\\\ 32^{\frac{3}{5}}\implies \sqrt[5]{32^3}\qquad \begin{cases} 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^5 \end{cases}\implies \sqrt[5]{(2^5)^3}\implies \sqrt[5]{(2^3)^5} \\\\\\ 2^3\implies 8$