Question

Rewrite both expressions using simplified rational exponents.

Answer 1

`~\hspace{7em}\textit{rational exponents} \\\\ a^{( n)/( m)} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-( n)/( m)} \implies \cfrac{1}{a^{( n)/( m)}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt[4]{81}~~ = ~~\sqrt[5]{243}\implies \sqrt[4]{81^1}~~ = ~~\sqrt[5]{243^1}\implies 81^{(1)/(4)}~~ = ~~243^{(1)/(5)}`