Question

What is an equivalent expression (m ^1/3)^ 1/5 *the fractions are powers btw*

Answer 1

$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( m^{\frac{1}{3}} \right)^{\frac{1}{5}}\implies m^{\frac{1}{3}\cdot \frac{1}{5}}\implies m^{\frac{1}{15}}\implies \sqrt[15]{m^1}\implies \sqrt[15]{m}$