Answers by visitors named: TK24NC

Raising the first equation to the fifth power, we get $a^5 b^{20} = 12^5 = 248832$. Dividing this equation by the second equation, we get $b^{15} = 32$, so $b = \sqrt[15]{32} = \sqrt[15]{2^5} = \sqrt[3]{2}$. Then from the first equation, \[a = \frac{12}{b...

The answer is 3 ^3sqrt4

Excuse me. If you are an AoPs worker, you wouldn't go and post that online trying to make it obvious.