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Simplify. Express your answer using a single exponent. $\newline$ $(6a^8)^2$

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Powers of a power: variable bases

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

\newline

(6a^8)^2

Apply power rule: Apply the power of a power rule to the expression $(6a^8)^2$ . The power of a power rule states that when raising a power to another power, you multiply the exponents. For a base number, the rule is $(b^n)^m = b^{n*m}$ . In this case, we have a base of $6$ and a base of $a^8$ , and we are raising both to the power of $2$ . $(6a^8)^2 = 6^2 \times (a^8)^2$
Calculate $6^2$ : Calculate $6^2$ . $\newline$ $6^2$ is $6$ multiplied by itself, which equals $36$ . $\newline$ $6^2 = 36$
Calculate $(a^8)^2$ : Calculate $(a^8)^2$ . Using the power of a power rule, we multiply the exponents $8$ and $2$ . $(a^8)^2 = a^{(8*2)} = a^{16}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $6^2 = 36$ and $(a^8)^2 = a^{16}$ , so we combine these to get the final simplified expression. $\newline$ $(6a^8)^2 = 36 \times a^{16}$

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