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

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Powers of a power: variable bases

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

\newline

(4z^3)^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 $(4z^3)^3$ , we apply this rule to the variable $z$ . $\newline$ $(4z^3)^3 = 4^3 \times (z^3)^3$
Calculate $4^3$ : Calculate $4^3$ . $\newline$ To simplify $4^3$ , we multiply $4$ by itself three times. $\newline$ $4^3 = 4 \times 4 \times 4 = 64$
Simplify $(z^3)^3$ : Simplify $(z^3)^3$ . We multiply the exponents for $z$ , which means $3$ times $3$ . $(z^3)^3 = z^{(3 \times 3)} = z^9$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $4^3 = 64$ and $(z^3)^3 = z^9$ . Now we combine these results to express the simplified form of the original expression. $\newline$ $(4z^3)^3 = 64 \times z^9$

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