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Simplify. Express your answer using a single exponent. $\newline$ $(11a^9)^2$

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Powers of a power: variable bases

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

\newline

(11a^9)^2

Apply power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have $(11a^9)^2$ , which means we need to square both the base $11$ and the exponent of $a^9$ . $\newline$ $(11a^9)^2 = 11^2 \times (a^9)^2$
Calculate $11^2$ : Calculate $11^2$ . $\newline$ To find $11^2$ , we multiply $11$ by itself. $\newline$ $11^2 = 11 \times 11 = 121$
Calculate $(a^9)^2$ : Calculate $(a^9)^2$ . $\newline$ To find $(a^9)^2$ , we multiply the exponent $9$ by $2$ . $\newline$ $(a^9)^2 = a^{(9 \times 2)} = a^{18}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ Now we combine the results to express the simplified form of the original expression. $\newline$ $(11a^9)^2 = 121 \times a^{18}$

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