How do I determine So the exponent that goes into the Box in the expression ( √(x) ) ^(6) = x ^(?)

Question

How do I determine So the exponent that goes into the Box in the expression


`( √(x) ) ^(6) = x ^(?)`

Answer 1

`\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}\\\\ \left( √(x) \right)^6\implies \left( \sqrt[2]{x^1} \right)^6\implies \left( x^{(1)/(2)} \right)^6\implies x^{(1)/(2)\cdot 6}\implies x^3`

Answer 2

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