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Simplify. Express your answer using a single exponent. $\newline$ $(3c^2)^2$

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Powers of a power: variable bases

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

\newline

(3c^2)^2

Apply power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that when you raise an exponent to another exponent, you multiply the exponents. In this case, we have $(3c^2)^2$ , which means we need to apply the exponent of $2$ to both $3$ and $c^2$ . $\newline$ $(3c^2)^2 = 3^2 \times (c^2)^2$
Calculate $3^2$ : Calculate $3^2$ . $\newline$ $3^2$ means $3$ multiplied by itself, which is $9$ . $\newline$ $3^2 = 9$
Calculate $(c^2)^2$ : Calculate $(c^2)^2$ . Using the power of a power rule, we multiply the exponents $2$ and $2$ . $(c^2)^2 = c^{(2*2)} = c^4$
Combine results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to get the final simplified expression. $\newline$ $(3c^2)^2 = 3^2 \times (c^2)^2 = 9c^4$

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