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

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Powers of a power: variable bases

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

\newline

(6w^8)^2

Apply power rule: Apply the power of a power rule to $(6w^8)^2$ . The power of a power rule states that when raising a power to another power, you multiply the exponents. For a base number $a$ and exponents $m$ and $n$ , $(a^m)^n = a^{m*n}$ . $(6w^8)^2 = 6^2 \times (w^8)^2$
Calculate $6^2$ : Calculate $6^2$ . $\newline$ $6^2 = 6 \times 6 = 36$
Calculate $(w^8)^2$ : Calculate $(w^8)^2$ . $(w^8)^2 = w^{(8*2)} = w^{16}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(6w^8)^2 = 6^2 \times (w^8)^2 = 36 \times w^{16}$
Write final expression: Write the final simplified expression. $\newline$ The final simplified expression is $36w^{16}$ .

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