Question

Simplify and give reasons:
${\left[{\left(\frac{3}{2}\right)}^{-2}\right]}^2$

• A. $\frac{16}{81}$
• B. $\frac{6}{81}$
• C. $\frac{16}{1}$
• D. None of these

Answer 1

Answer: (A)

$\frac{16}{81}$

we know that,

$\because (a^m{)}^n=a^{mn}$

so,

$\left(\right(\frac{3}{2}{)}^{-2}{)}^2=(\frac{3}{2}{)}^{-4}$

we also know

$\because (\frac{a}{b}{)}^{-m}=(\frac{b}{a}{)}^m$

$=(\frac{2}{3}{)}^4$

$=\frac{16}{81}$