Question

Simplify:
$\frac{{\left(15\right)}^{-3}\times {(-12)}^4}{5^{-6}\times {36}^2}$

Answer 1

$\frac{{\left(15\right)}^{-3}\times {(-12)}^4}{5^{-6}\times {36}^2}$

$=\frac{{(5\times 3)}^{-3}\times {(-12)}^4}{5^{-6}\times {(12\times 3)}^2}$

$=\frac{5^{-3}\times 3^{-3}\times {(-12)}^4}{5^{-6}\times {12}^2\times 3^2}$ (using${\left(xy\right)}^n=x^n.y^n$

$=5^{(-3+6)}\times 3^{(-3-2)}\times {(-12)}^{(4-2)}$

$=\frac{5^3\times {(-12)}^2}{3^5}$

$=\frac{125\times 144}{243}$

$=\frac{2000}{27}$