Question

Identify which of the following in NOT equivalent to

`2 (2)/(3)`
​

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] \rule{34em}{0.25pt}`

`\boxed{A}\qquad \sqrt[4]{8}\implies \sqrt[4]{2^3}\implies 2^{(3)/(4)} \\\\\\ \boxed{B}\qquad \sqrt[4]{2^3}\implies 2^{(3)/(4)} \\\\\\ \boxed{C}\qquad 2^{(1)/(4)}* 2^{(1)/(2)}\implies 2^{(1)/(4)+(1)/(2)}\implies 2^{(1+2)/(4)}\implies 2^{(3)/(4)} \\\\\\ \boxed{D}\qquad \left( 2^{(1)/(4)} \right)^{(1)/(2)}\implies 2^{(1)/(4)\cdot (1)/(2)}\implies 2^{(1)/(8)}\qquad \textit{\large \checkmark}`