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

Simplify $(2 \cdot 3)^{4}$.
  1. $2^{4} + 3^{4}$
  2. $2^{4} \cdot 3^{4} = 1296$
  3. $5^{4}$
  4. $6^{16}$

Solution

Use $(ab)^{n} = a^{n} b^{n}$. $(2 \cdot 3)^{4} = 6^{4} = 1296 = 16 \cdot 81 = 2^{4} \cdot 3^{4}$.

Asked in: IMO

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