Simplify $\dfrac{a^{8} \cdot a^{-3}}{a^{2}}$.

Simplify $\dfrac{a^{8} \cdot a^{-3}}{a^{2}}$.
  1. $a^{3}$
  2. $a^{7}$
  3. $a^{13}$
  4. $a^{-3}$

Solution

Numerator: $a^{8} \cdot a^{-3} = a^{8-3} = a^{5}$. Then $\dfrac{a^{5}}{a^{2}} = a^{5-2} = a^{3}$.

Asked in: IMO

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