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Simplify. Express your answer using a single exponent. $\newline$ $(12a^4)^2$

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Powers of a power: variable bases

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

\newline

(12a^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. $\newline$ $(12a^4)^2 = 12^2 \times (a^4)^2$
Calculate Square of $12$ : Calculate the square of $12$ . $12^2 = 12 \times 12 = 144$
Multiply Exponents for Variable: Multiply the exponents for the variable $a$ . $(a^4)^2 = a^{(4 \times 2)} = a^8$
Combine Results: Combine the results from Step $2$ and Step $3$ . $144 \times a^8$

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