What is the reduced radical form of: ((x^(1/2)*x^(5/12) )^4)/(x^(2/3))

Question

What is the reduced radical form of:


`((x^(1/2)*x^(5/12) )^4)/(x^(2/3))`

Answer 1

`\begin{array}{llll} \hspace{5em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} \end{array} ~\hfill~ \begin{array}{llll} \textit{rational exponents} \\\\ a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill`

`\cfrac{(x^{(1)/(2)}x^{(5)/(12)})^4}{x^{(2)/(3)}}\implies \cfrac{(x^{(1)/(2)+(5)/(12)})^4}{x^{(2)/(3)}}\implies \cfrac{(x^{(11)/(12)})^4}{x^{(2)/(3)}} \implies \cfrac{x^{(11)/(12)\cdot 4}}{x^{(2)/(3)}}\implies \cfrac{x^{(11)/(3)}}{x^{(2)/(3)}} \\\\\\ x^{(11)/(3)}\cdot x^{-(2)/(3)}\implies x^{(11)/(3)-(2)/(3)}\implies x^{(9)/(3)}\implies {\Large \begin{array}{llll} x^3 \end{array}}`