Answer
true
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $\left(\dfrac{a}{b}\right)^m = \dfrac{a^m}{b^m}$
Use the rule (1) above to obtain:
$(\frac{2}{3})^{-2} = \dfrac{1}{(\frac{2}{3})^2}$
Use rule (2) above to obtain:
$=\dfrac{1}{(\frac{2^2}{3^2})}$
Use the rule $a \div \frac{b}{c}=a \cdot \frac{c}{b}$ to obtain:
$=1 \cdot \left(\frac{3^2}{2^2}\right)
\\=\dfrac{3^2}{2^2}$
Use rule (2) above to obtain:
$=\left(\dfrac{3}{2}\right)^2$
Thus, the given statement is true.
