Answer
$\left(1^4\right)^5=1^{20}$
$1^{20}=1$
Work Step by Step
$\left(a^m\right)^n = a^{mn}$
Thus,
$\left(1^4\right)^5
\\= 1^{4\cdot 5}
\\=1^{20}
\\=1$
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