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Simplify. Express your answer using a single exponent. $\newline$ $(7q^8)^2$

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Powers of a power: variable bases

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

\newline

(7q^8)^2

Apply Power Rule: Apply the power to a power rule. $\newline$ When raising a power to another power, we multiply the exponents. We also raise the numerical coefficient to the power of $2$ . $\newline$ $(7q^8)^2 = 7^2 \times (q^8)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(q^8)^2$ : Calculate $(q^8)^2$ . $(q^8)^2 = q^{(8 \times 2)} = q^{16}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(7q^8)^2 = 49 \times q^{16}$

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