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

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Powers of a power: variable bases

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

\newline

(7b^6)^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 $(7b^6)^2$ , which means we need to apply the exponent of $2$ to both $7$ and $b^6$ . $\newline$ $(7b^6)^2 = 7^2 \times (b^6)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ $7^2$ is $7$ multiplied by itself. $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(b^6)^2$ : Calculate $(b^6)^2$ . Using the power of a power rule, we multiply the exponents $6$ and $2$ . $(b^6)^2 = b^{(6 \times 2)} = b^{12}$
Combine results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to express the simplified form of the original expression. $\newline$ $(7b^6)^2 = 49 \times b^{12} = 49b^{12}$

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