Express $(2^{3} \cdot 3^{2})^{2}$ in expanded power form.

Express $(2^{3} \cdot 3^{2})^{2}$ in expanded power form.
  1. $2^{6} \cdot 3^{4}$
  2. $2^{5} \cdot 3^{4}$
  3. $2^{6} \cdot 3^{2}$
  4. $6^{12}$

Solution

$(2^{3} \cdot 3^{2})^{2} = 2^{3 \cdot 2} \cdot 3^{2 \cdot 2} = 2^{6} \cdot 3^{4}$.

Asked in: IMO

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