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

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Powers of a power: variable bases

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

\newline

(6y^6)^2

Apply power rule: Apply the power to a power rule. $\newline$ The power to a power rule states that when you raise a power to another power, you multiply the exponents. In this case, we have $(6y^6)^2$ , which means we need to apply the exponent of $2$ to both the base $6$ and the exponent of $y^6$ . $\newline$ $(6y^6)^2 = 6^2 \times (y^6)^2$
Calculate $6^2$ : Calculate $6^2$ . To find $6^2$ , we multiply $6$ by itself. $6^2 = 6 \times 6 = 36$
Calculate $(y^6)^2$ : Calculate $(y^6)^2$ . To find $(y^6)^2$ , we multiply the exponent $6$ by the outer exponent $2$ . $(y^6)^2 = y^{(6 \times 2)} = y^{12}$
Combine results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to get the final simplified expression. $\newline$ $(6y^6)^2 = 36 \times y^{12}$

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