Simplify $\dfrac{3^{-1} \cdot 5^{2}}{3 \cdot 5^{-1}}$.

Simplify $\dfrac{3^{-1} \cdot 5^{2}}{3 \cdot 5^{-1}}$.
  1. $\dfrac{125}{9}$
  2. $\dfrac{125}{15}$
  3. $\dfrac{15}{125}$
  4. $\dfrac{9}{125}$

Solution

Group bases: $3^{-1-1} \cdot 5^{2-(-1)} = 3^{-2} \cdot 5^{3} = \dfrac{125}{9}$.

Asked in: IMO

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