Question

Simplify cube root of 7 over fifth root of 7.

Answer 1

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ \cfrac{\sqrt[3]{7}}{\sqrt[5]{7}}\implies \cfrac{\sqrt[3]{7^1}}{\sqrt[5]{7^1}}\implies \cfrac{7^{\frac{1}{3}}}{7^{\frac{1}{5}}}\implies 7^{\frac{1}{3}}\cdot 7^{-\frac{1}{5}}\implies 7^{\frac{1}{3}-\frac{1}{5}} \\\\\\ 7^{\frac{5-3}{15}}\implies 7^{\frac{2}{15}}$