Simplify $\dfrac{(a^{2} b^{3})^{4}}{(a^{3} b^{2})^{2}}$.

Simplify $\dfrac{(a^{2} b^{3})^{4}}{(a^{3} b^{2})^{2}}$.
  1. $a^{2} b^{8}$
  2. $a^{14} b^{16}$
  3. $a^{8} b^{12}$
  4. $a^{2} b^{6}$

Solution

Numerator: $(a^{2} b^{3})^{4} = a^{8} b^{12}$. Denominator: $(a^{3} b^{2})^{2} = a^{6} b^{4}$. Divide: $a^{8-6} b^{12-4} = a^{2} b^{8}$.

Asked in: IMO

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