Question

Pre calc
combine radicals/fractional exponents

Answer 1

`\begin{array}{llll} ~\hspace{7em}\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{6x^(-1)y^(-1)}{\sqrt[4]{xy^4}}\implies \cfrac{6x^(-1)y^(-1)}{\left( xy^4 \right)^{(1)/(4)} }\implies \cfrac{6x^(-1)y^(-1)}{x^{(1)/(4)} y^{4\cdot (1)/(4)}}\implies \cfrac{6x^(-1)y^(-1)}{x^{(1)/(4)} y^1}\implies \cfrac{6x^(-1)y^(-1)x^{-(1)/(4)} y^(-1)}{1}`

`6x^(-1)x^{-(1)/(4)}y^(-1) y^(-1)\implies 6x^{-1-(1)/(4)} y^(-1-1)\implies {\Large \begin{array}{llll} \underset{\textit{\small a}}{6} \stackrel{\textit{\small ~~ b}}{x^{-(5)/(4)}} \stackrel{\textit{\small ~~ c}}{y^(-2)} \end{array}}`