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

Find the value of $\left[(-3)^{-2}\right]^{2}$.
  1. $-\dfrac{1}{81}$
  2. $\dfrac{1}{81}$
  3. $81$
  4. $9$

Solution

$(-3)^{-2 \cdot 2} = (-3)^{-4} = \dfrac{1}{(-3)^{4}} = \dfrac{1}{81}$ (even power of negative is positive).

Asked in: IMO

Practice more EXPONENTS AND POWERS questions on Aicharya