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

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Powers of a power: variable bases

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

\newline

(2h^3)^3

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 $(2h^3)^3$ , which means we need to raise both $2$ and $h^3$ to the power of $3$ . $\newline$ $(2h^3)^3 = 2^3 \times (h^3)^3$
Calculate $2^3$ : Calculate $2^3$ . $\newline$ $2^3$ means $2$ multiplied by itself $3$ times. $\newline$ $2^3 = 2 \times 2 \times 2 = 8$
Calculate $(h^3)^3$ : Calculate $(h^3)^3$ . Using the power of a power rule, we multiply the exponents $3$ and $3$ . $(h^3)^3 = h^{(3*3)} = h^9$
Combine results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to get the final simplified expression. $\newline$ $(2h^3)^3 = 2^3 \times h^9 = 8h^9$

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