Question

How do I determine So the exponent that goes into the Box in the expression
$( \sqrt{x} ) ^{6} = x ^{?}$

Answer 1

x^ 1/2^6 =

the sqrt root is the same as 1/2

power to a power means multipl

x^ (1/2*6)

x^3

Answer 2

$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \sqrt{x} \right)^6\implies \left( \sqrt[2]{x^1} \right)^6\implies \left( x^{\frac{1}{2}} \right)^6\implies x^{\frac{1}{2}\cdot 6}\implies x^3$