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Simplify. Express your answer using a single exponent. $\newline$ $(8q^4)^2$

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Powers of a power: variable bases

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

\newline

(8q^4)^2

Apply Power Separately: Apply the power to both the coefficient and the variable separately. $\newline$ When raising a power to a power, we multiply the exponents, and when raising a number to a power, we simply calculate the number to that power. $\newline$ $(8q^4)^2 = 8^2 \times (q^4)^2$
Calculate $8^2$ : Calculate $8^2$ . $\newline$ $8^2 = 8 \times 8 = 64$
Calculate $(q^4)^2$ : Calculate $(q^4)^2$ . $\newline$ When raising a power to another power, we multiply the exponents. $\newline$ $(q^4)^2 = q^{(4 \times 2)} = q^8$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(8q^4)^2 = 8^2 \times (q^4)^2 = 64 \times q^8$
Write Final Expression: Write the final simplified expression. $\newline$ The expression $(8q^4)^2$ simplifies to $64q^8$ .

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