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

Simplify $\left(\dfrac{3^{4}}{3^{2}}\right)^{3}$.
  1. $3^{4}$
  2. $3^{6} = 729$
  3. $3^{12}$
  4. $9^{3}$

Solution

Inside: $\dfrac{3^{4}}{3^{2}} = 3^{4-2} = 3^{2}$. Then $(3^{2})^{3} = 3^{6} = 729$.

Asked in: IMO

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