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

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Powers of a power: variable bases

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

\newline

(2b^4)^2

Apply power rule: Apply the power of a power rule to $(2b^4)^2$ . The power of a power rule states that $(a^n)^m = a^{n*m}$ . We will apply this rule to both the coefficient $2$ and the variable $b$ with its exponent $4$ . $(2b^4)^2 = 2^2 \times (b^4)^2$
Calculate $2^2$ : Calculate $2^2$ . $\newline$ $2^2 = 2 \times 2 = 4$
Calculate $(b^4)^2$ : Calculate $(b^4)^2$ using the power of a power rule. $\newline$ $(b^4)^2 = b^{(4*2)} = b^8$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $2^2 = 4$ and $(b^4)^2 = b^8$ , so we combine these to get the final simplified expression. $\newline$ $(2b^4)^2 = 4b^8$

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