If $a = 2^{p}$, $b = 2^{q}$, $c = 2^{p+q}$, then $abc$ equals

If $a = 2^{p}$, $b = 2^{q}$, $c = 2^{p+q}$, then $abc$ equals
  1. $2^{p+q}$
  2. $2^{2(p+q)}$
  3. $2^{p+q+pq}$
  4. $2^{pq}$

Solution

$abc = 2^{p} \cdot 2^{q} \cdot 2^{p+q} = 2^{p + q + (p+q)} = 2^{2(p+q)}$.

Asked in: IMO

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