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

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Powers of a power: variable bases

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

\newline

(2g^3)^3

Apply Power Rule: Apply the power of a power rule to the expression $(2g^3)^3$ . The power of a power rule states that $(a^m)^n = a^{m*n}$ . We will apply this rule to both the numerical coefficient and the variable with its exponent. $(2g^3)^3 = 2^3 \times (g^3)^3$
Calculate $2^3$ : Calculate the value of $2^3$ . $\newline$ $2^3 = 2 \times 2 \times 2 = 8$
Apply Power Rule to $g^3$ : Apply the power of a power rule to $(g^3)^3$ . $\newline$ $(g^3)^3 = g^{(3*3)} = g^9$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $2^3 = 8$ and $(g^3)^3 = g^9$ , so we combine these to get the final simplified expression. $\newline$ $(2g^3)^3 = 8g^9$

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