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Simplify. Express your answer using a single exponent. $\newline$ $(12a^9)^2$

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Powers of a power: variable bases

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

\newline

(12a^9)^2

Apply power separately: Apply the power to both the coefficient and the variable separately. $\newline$ When raising a power to a power, we multiply the exponents, and when raising a number to a power, we simply calculate the number to that power. $\newline$ $(12a^9)^2 = 12^2 \times (a^9)^2$
Calculate $12^2$ : Calculate $12^2$ . $\newline$ $12^2 = 12 \times 12 = 144$
Calculate $(a^9)^2$ : Calculate $(a^9)^2$ . $\newline$ When raising a power to another power, we multiply the exponents. $\newline$ $(a^9)^2 = a^{(9 \times 2)} = a^{18}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(12a^9)^2 = 144 \times a^{18}$

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