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Simplify. Express your answer using a single exponent. $\newline$ $(11v^6)^2$

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Powers of a power: variable bases

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

\newline

(11v^6)^2

Apply Power Rule: Apply the power of a power rule to $(11v^6)^2$ . When raising a power to another power, we multiply the exponents. We also raise the numerical coefficient to the power of $2$ . $(11v^6)^2 = 11^2 \times (v^6)^2$
Calculate $11^2$ : Calculate $11^2$ . $\newline$ $11^2 = 11 \times 11 = 121$
Calculate $(v^6)^2$ : Calculate $(v^6)^2$ . $(v^6)^2 = v^{(6 \times 2)} = v^{12}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(11v^6)^2 = 121 \times v^{12}$
Write Final Expression: Write the final simplified expression. $\newline$ The expression $(11v^6)^2$ simplifies to $121v^{12}$ .

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