Simplify $\left(\dfrac{2}{3}\right)^{4} \cdot \left(\dfrac{3}{2}\right)^{4}$.

Simplify $\left(\dfrac{2}{3}\right)^{4} \cdot \left(\dfrac{3}{2}\right)^{4}$.
  1. $0$
  2. $1$
  3. $\left(\dfrac{2}{3}\right)^{8}$
  4. $\dfrac{1}{6}$

Solution

$\left(\dfrac{2}{3} \cdot \dfrac{3}{2}\right)^{4} = 1^{4} = 1$.

Asked in: IMO

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