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

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Powers of a power: variable bases

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

\newline

(11y^3)^2

Apply Power to Base and Exponent: Apply the power to both the base number and the exponent of the variable. $\newline$ 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. $\newline$ $(11y^3)^2 = 11^2 \times (y^3)^2$
Calculate $11^2$ : Calculate $11^2$ . $\newline$ $11^2 = 11 \times 11 = 121$
Calculate $(y^3)^2$ : Calculate $(y^3)^2$ . $\newline$ When raising a power to another power, we multiply the exponents. $\newline$ $(y^3)^2 = y^{(3 \times 2)} = y^6$
Combine Results for Final Expression: Combine the results from Step $2$ and Step $3$ to write the final simplified expression. $\newline$ $(11y^3)^2 = 121 \times y^6 = 121y^6$

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