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Simplify. Express your answer using a single exponent. $\newline$ $(11p^3)^2$

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Powers of a power: variable bases

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

\newline

(11p^3)^2

Apply power rule: Apply the power of a power rule to \(11p^ $3$ )^ $2$ \. The power of a power rule states that a^m)^n = a^{m*n}\. We will apply this rule to both the numerical part and the variable part of the expression. \(\(11p^ $3$ )^ $2$ = $11$ ^ $2$ * (p^ $3$ )^ $2$
Calculate $11^2$ : Calculate $11^2$ . $\newline$ $11^2 = 11 \times 11 = 121$
Calculate $(p^3)^2$ : Calculate $(p^3)^2$ using the power of a power rule. $\newline$ $(p^3)^2 = p^{(3*2)} = p^6$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ The simplified expression is $121 \times p^6$ .

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