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Simplify. Express your answer using a single exponent. $\newline$ $(4w^5)^2$

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Powers of a power: variable bases

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

\newline

(4w^5)^2

Apply power to factors: Apply the power to each factor inside the parentheses. $\newline$ $(4w^5)^2 = 4^2 \times (w^5)^2$
Calculate $4^2$ : Calculate $4^2$ . $\newline$ $4^2 = 16$
Apply power rule for exponents: Apply the power rule for exponents $(a^m)^n = a^{m*n}$ . $\newline$ $(w^5)^2 = w^{5*2} = w^{10}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $16 \times w^{10} = 16w^{10}$

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