Question

The value of $\left(\right(\frac{3}{2}{)}^{-1}{)}^{-2}$ is _____.

• A. $\frac{4}{9}$
• B. $\frac{9}{4}$
• C. $\frac{4}{4}$
• D. $\frac{9}{9}$

Answer 1

The correct option is B $\frac{9}{4}$

As we know $(a^m{)}^n=a^{mn}$
$\Rightarrow$ $\left(\right(\frac{3}{2}{)}^{-1}{)}^{-2}=(\frac{3}{2}{)}^{-1\times -2}$

$=(\frac{3}{2}{)}^2=\frac{3^2}{2^2}=\frac{9}{4}$ $(\because (\frac{a}{b}{)}^m=\frac{a^m}{b^m})$