Question

Help??

Find the value of:


A. (4/25)^1/2

B. (4/25)^-1/2

Answer 1

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

`\left( \cfrac{4}{25} \right)^{(1)/(2)}\implies \sqrt[2]{\left( \cfrac{4}{25} \right)^1}\implies \sqrt{\cfrac{4}{25}}\implies \cfrac{√(4)}{√(25)}\implies \cfrac{2}{5} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{4}{25} \right)^{-(1)/(2)}\implies \left( \cfrac{25}{4} \right)^{(1)/(2)}\implies \cfrac{√(25)}{√(4)}\implies \cfrac{5}{2}`