Question

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

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

Answer 1

The correct option is D

$\frac{9}{4}$

Since $(a^m{)}^n=a^{mn}$ for integers $a,m$ and $n$ $(a\ne 0)$
$({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}=(\frac{3}{2}{)}^{-1\times -2}$
$={\left(\frac{3}{2}\right)}^2$
$=\frac{3^2}{2^2}(\because \frac{a^m}{b^m}=(\frac{a}{b}{)}^m)$
$=\frac{9}{4}$