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

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Powers of a power: variable bases

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

\newline

(7c^7)^2

Apply Power Rule: Apply the power of a power rule to the expression $(7c^7)^2$ . 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 both $7$ and $c^7$ . $(7c^7)^2 = 7^2 \times (c^7)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ $7^2$ is $7$ multiplied by itself, which equals $49$ . $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(c^7)^2$ : Calculate $(c^7)^2$ . Using the power of a power rule, we multiply the exponents $7$ and $2$ . $(c^7)^2 = c^{(7 \times 2)} = c^{14}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $7^2 = 49$ and $(c^7)^2 = c^{14}$ . Now we combine these to express the simplified form of the original expression. $\newline$ $(7c^7)^2 = 49c^{14}$

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