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Simplify. Express your answer using a single exponent. $\newline$ $(7a^6)^2$

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Powers of a power: variable bases

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

\newline

(7a^6)^2

Apply power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that when you raise a power to another power, you multiply the exponents. In this case, we have $(7a^6)^2$ , which means we need to apply the exponent of $2$ to both $7$ and $a^6$ . $\newline$ $(7a^6)^2 = 7^2 \times (a^6)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ To simplify $7^2$ , we multiply $7$ by itself. $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(a^6)^2$ : Calculate $(a^6)^2$ . To simplify $(a^6)^2$ , we multiply the exponents $(6$ and $2)$ . $(a^6)^2 = a^{(6 \times 2)} = a^{12}$
Combine results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to get the final simplified expression. $\newline$ $(7a^6)^2 = 49 \times a^{12} = 49a^{12}$

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