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Simplify. Express your answer using a single exponent. $\newline$ $(7s^9)^2$

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Powers of a power: variable bases

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

\newline

(7s^9)^2

Apply Power Rule: Apply the power of a power rule to $(7s^9)^2$ . The power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have an exponent of $2$ being applied to both $7$ and $s^9$ . $(7s^9)^2 = 7^2 \times (s^9)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ $7^2$ is $7$ multiplied by itself. $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(s^9)^2$ : Calculate $(s^9)^2$ . Using the power of a power rule, we multiply the exponents $9$ and $2$ . $(s^9)^2 = s^{(9 \times 2)} = s^{18}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $49$ for $7^2$ and $s^{18}$ for $(s^9)^2$ , so we combine them to get the final simplified expression. $\newline$ $(7s^9)^2 = 49s^{18}$

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