Find the remainder when $16^{ 15^{ 12 } }$ is divided by 13.

The answer is 1.

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Since $15$ is divisible by $3$ , so is $15^{12}$ . Then $15^{12}=3n$ for some positive integer $n$ . We compute

$16^{15^{12}}\equiv 3^{3n}=27^n\equiv 1^n=\boxed{1}\pmod{13}$ .