Question

Given: $(32{)}^{\frac{-2}{5}}÷(125{)}^{\frac{-2}{3}}$ is $m\frac{1}{4}$, then $m$ is?

Answer 1

$(32{)}^{-\frac{2}{5}}÷(125{)}^{-\frac{2}{3}}$
$=(2^5{)}^{-\frac{2}{5}}÷(5^3{)}^{-\frac{2}{3}}$
$=(2{)}^{-\frac{2\times 5}{5}}÷(5{)}^{-\frac{2\times 3}{3}}$
$=2^{-2}÷5^{-2}$
$=(\frac{2}{5}{)}^{-2}$
$=(\frac{5}{2}{)}^2$
$=\frac{25}{4}$
$=6\frac{1}{4}$

Thus, $m=6$.