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

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Powers of a power: variable bases

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

\newline

(7d^8)^2

Apply Power Rule: Apply the power of a power rule to the expression $(7d^8)^2$ . The power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have an exponent of $2$ being applied to $d^8$ . $(7d^8)^2 = 7^2 \times (d^8)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ $7^2$ is $7$ multiplied by itself. $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(d^8)^2$ : Calculate $(d^8)^2$ . Using the power of a power rule, we multiply the exponents $8$ and $2$ . $(d^8)^2 = d^{(8 \times 2)} = d^{16}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $7^2 = 49$ and $(d^8)^2 = d^{16}$ . Now we combine these to express the original expression as a single exponent. $\newline$ $(7d^8)^2 = 49d^{16}$

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