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

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Powers of a power: variable bases

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

\newline

(9m^2)^2

Apply power rule: Apply the power of a power rule to the expression $(9m^2)^2$ . 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 $9$ and $m^2$ . $(9m^2)^2 = 9^2 \times (m^2)^2$
Calculate $9^2$ : Calculate $9^2$ . $9^2$ is $9$ multiplied by itself, which equals $81$ . $9^2 = 81$
Calculate $(m^2)^2$ : Calculate $(m^2)^2$ . Using the power of a power rule, we multiply the exponents. The base $m$ has an exponent of $2$ , and we are raising it to the power of $2$ , so we get $m^{(2*2)}$ . $(m^2)^2 = m^{(2*2)} = m^4$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $9^2 = 81$ and $(m^2)^2 = m^4$ . Now we combine these to get the final simplified expression. $\newline$ $(9m^2)^2 = 81 \times m^4$
Write final answer: Write the final answer. $\newline$ The expression $(9m^2)^2$ simplifies to $81m^4$ .

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