Answer
$9$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$
Use rule (1) above to obtain:
$\frac{1}{3})^{-2} = \dfrac{1}{(\frac{1}{3})^2}$
Use rule (3) above to obtain:
$=\dfrac{1}{\frac{1^2}{3^2}}
\\=\dfrac{1}{\frac{1}{9}}$
Use the rule $a \div \dfrac{b}{c} = a \cdot \dfrac{c}{b}$ to obtain:
$=1 \cdot \dfrac{9}{1}
\\=9$
