Question

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

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

Answer 1

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

We have $(a^m{)}^n=a^{mn}$ for a non-zero integer $a$ and any integers $m$ and $n.$
$⟹({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}={\left(\frac{3}{2}\right)}^{-1\times -2}$
$=(\frac{3}{2}{)}^2$
$=\frac{9}{4}$