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Simplify. Express your answer as the given base raised to a single exponent. $\newline$ $(1^5)^8$

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Power of a power: integer bases

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Q. Simplify. Express your answer as the given base raised to a single exponent.

\newline

(1^5)^8

Identify base and exponents: Step $1$ : Identify the base and the exponents in the expression. $\newline$ In $(1^5)^8$ , $1$ is the base raised to the exponents $5$ and $8$ . $\newline$ Base: $1$ $\newline$ Exponents: $5$ , $8$
Apply power of power rule: Step $2$ : Apply the power of a power rule, which states $(a^m)^n = a^{(m*n)}$ . $\newline$ $(1^5)^8$ $\newline$ = $1^{(5*8)}$ $\newline$ = $1^{40}$
Simplify expression: Step $3$ : Simplify $1^{40}$ . $\newline$ Since any non-zero number raised to any power is itself, $1$ raised to any power is $1$ . $\newline$ $1^{40} = 1$

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