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Simplify. Express your answer using a single exponent. $\newline$ $(2w^4)^3$

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Powers of a power: variable bases

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

\newline

(2w^4)^3

Apply Power Rule: Apply the power to a power rule. $\newline$ When raising a power to another power, we multiply the exponents. For the given expression $(2w^4)^3$ , we apply this rule to the variable $w$ with the exponent $4$ being raised to the power of $3$ . $\newline$ $(2w^4)^3 = 2^3 \times (w^4)^3$
Calculate $2^3$ : Calculate $2^3$ . We calculate the cube of $2$ to simplify the constant part of the expression. $2^3 = 2 \times 2 \times 2 = 8$
Calculate $(w^4)^3$ : Calculate $(w^4)^3$ . We multiply the exponents for the variable $w$ . $(w^4)^3 = w^{(4 \times 3)} = w^{12}$
Combine Results: Combine the results. $\newline$ We combine the simplified constant part and the variable part to get the final simplified expression. $\newline$ $(2w^4)^3 = 2^3 \times (w^4)^3 = 8 \times w^{12} = 8w^{12}$

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