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

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Powers of a power: variable bases

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

\newline

(3h^3)^2

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that when you raise a power to another power, you multiply the exponents. In this case, we have $(3h^3)^2$ , which means we need to apply the exponent of $2$ to both the coefficient $3$ and the variable $h^3$ . $\newline$ $(3h^3)^2 = 3^2 \times (h^3)^2$
Calculate $3^2$ : Calculate $3^2$ . $\newline$ To simplify $3^2$ , we multiply $3$ by itself. $\newline$ $3^2 = 3 \times 3 = 9$
Calculate $(h^3)^2$ : Calculate $(h^3)^2$ . $\newline$ To simplify $(h^3)^2$ , we multiply the exponents $3$ and $2$ . $\newline$ $(h^3)^2 = h^{(3*2)} = h^6$
Combine Results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to get the final simplified expression. $\newline$ $(3h^3)^2 = 3^2 \times (h^3)^2 = 9h^6$

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