Question

When 9^2/3 is written in simplest radicsl form, which value remains under the radical? 3 6 9 27

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}\\\\ 9^{\frac{2}{3}}\implies (3^2)^{\frac{2}{3}}\implies 3^{2\cdot \frac{2}{3}}\implies 3^{\frac{4}{3}}\implies \sqrt[3]{3^4}\implies \sqrt[3]{3^3\cdot 3^1}\implies 3\sqrt[3]{\stackrel{\textit{this one}}{3}}

Explanation:

Answer 2

`\bf ~\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] \rule{34em}{0.25pt}\\\\ 9^{(2)/(3)}\implies (3^2)^{(2)/(3)}\implies 3^{2\cdot (2)/(3)}\implies 3^{(4)/(3)}\implies \sqrt[3]{3^4}\implies \sqrt[3]{3^3\cdot 3^1}\implies 3\sqrt[3]{\stackrel{\textit{this one}}{3}}`