Question

Simplify :
${\left(\frac{{15}^{\frac{1}{3}}}{9^{\frac{1}{4}}}\right)}^{-6}$

Answer 1

${\left(\frac{{15}^{\frac{1}{3}}}{9^{\frac{1}{4}}}\right)}^{-6}$

$=\frac{{\left({15}^{\frac{1}{3}}\right)}^{-6}}{{\left(9^{\frac{1}{4}}\right)}^{-6}}$

$=\frac{{15}^{-\frac{6}{3}}}{9^{-\frac{6}{4}}}$

$=\frac{{15}^{-2}}{9^{-\frac{3}{2}}}$

$=\frac{9^{\frac{3}{2}}}{{15}^2}$

$=\frac{{\left(3^2\right)}^{\frac{3}{2}}}{(3\times 5{)}^2}$

$=\frac{3^3}{3^2\times 5^2}$

$=\frac{3}{5^2}$

$=\frac{3}{25}$