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Simplify. Express your answer using a single exponent. $\newline$ $(4s^9)^4$

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Powers of a power: variable bases

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

\newline

(4s^9)^4

Apply Power Rule: Apply the power of a power rule to the expression $(4s^9)^4$ . 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 $4$ being applied to both $4$ and $s^9$ . $(4s^9)^4 = 4^4 \times (s^9)^4$
Calculate $4^4$ : Calculate $4^4$ . $\newline$ $4^4$ is $4$ multiplied by itself $4$ times. $\newline$ $4^4 = 4 \times 4 \times 4 \times 4 = 256$
Apply Power Rule: Apply the power of a power rule to $(s^9)^4$ . We multiply the exponents $9$ and $4$ to get the new exponent for $s$ . $(s^9)^4 = s^{(9 \times 4)} = s^{36}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $4^4 = 256$ and $(s^9)^4 = s^{36}$ . Now we combine these results to express the simplified form of the original expression. $\newline$ $(4s^9)^4 = 256 \times s^{36}$

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