Evaluate $\left(\dfrac{2}{3}\right)^{-2}$.

Evaluate $\left(\dfrac{2}{3}\right)^{-2}$.
  1. $\dfrac{4}{9}$
  2. $\dfrac{9}{4}$
  3. $-\dfrac{4}{9}$
  4. $\dfrac{1}{9}$

Solution

$\left(\dfrac{a}{b}\right)^{-n} = \left(\dfrac{b}{a}\right)^{n}$. So $\left(\dfrac{2}{3}\right)^{-2} = \left(\dfrac{3}{2}\right)^{2} = \dfrac{9}{4}$.

Asked in: IMO

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