Question

If $x={\left(\frac{3}{2}\right)}^2\times {\left(\frac{2}{3}\right)}^{-4}$, then $x^{-2}=$ equals:

Answer 1

$x={\left(\frac{3}{2}\right)}^2\times {\left(\frac{2}{3}\right)}^{-4}$
$x={\left(\frac{3}{2}\right)}^2\times \frac{2^{-4}}{3^{-4}}$
$(\because {\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m})$
$x=\frac{3^2}{2^2}\times \frac{3^4}{2^4}=\frac{3^{2+4}}{2^{2+4}}=\frac{3^6}{2^6}={\left(\frac{3}{6}\right)}^6$
$x={\left(\frac{3}{6}\right)}^6$
$x^{-2}={\left({\left(\frac{3}{6}\right)}^6\right)}^{-2}={\left(\frac{3}{6}\right)}^{12}=\frac{3^{-12}}{2^{-12}}=\frac{2^{12}}{3^{12}}={\left(\frac{2}{3}\right)}^{12}$