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Simplify. Express your answer using a single exponent. $\newline$ $(5s^9)^2$

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Powers of a power: variable bases

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Q. Simplify. Express your answer using a single exponent.

\newline

(5s^9)^2

Apply Power Rule: Apply the power of a power rule to $(5s^9)^2$ . The power of a power rule states that $(a^m)^n = a^{m*n}$ . Therefore, we need to apply the exponent of $2$ to both the base $5$ and the exponent of $s^9$ . $(5s^9)^2 = 5^2 \cdot (s^9)^2$
Calculate $5^2$ : Calculate $5^2$ . $\newline$ $5^2$ is $5$ multiplied by itself, which equals $25$ . $\newline$ $5^2 = 25$
Calculate $(s^9)^2$ : Calculate $(s^9)^2$ . Using the power of a power rule, we multiply the exponents $9$ and $2$ . $(s^9)^2 = s^{(9*2)} = s^{18}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $5^2 = 25$ and $(s^9)^2 = s^{18}$ , so we multiply these together to get the final simplified expression. $\newline$ $(5s^9)^2 = 25 \times s^{18} = 25s^{18}$

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