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Simplify. Express your answer using a single exponent. $\newline$ $(7y^6)^2$

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Powers of a power: variable bases

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

\newline

(7y^6)^2

Apply power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that when you raise a power to another power, you multiply the exponents. In this case, we have $(7y^6)^2$ , which means we will raise $7$ to the power of $2$ and $y^6$ to the power of $2$ . $\newline$ $(7y^6)^2 = 7^2 \times (y^6)^2$
Calculate $7^2$ : Calculate $7^2$ . $7^2$ means $7$ multiplied by itself, which is $49$ . $7^2 = 49$
Calculate $(y^6)^2$ : Calculate $(y^6)^2$ . Using the power of a power rule, we multiply the exponents. So, $(y^6)^2$ becomes $y^{(6*2)}$ , which is $y^{12}$ . $(y^6)^2 = y^{(6*2)} = y^{12}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ Now we combine the results to express the original expression using a single exponent. $\newline$ $(7y^6)^2 = 49 \times y^{12}$
Write final expression: Write the final simplified expression. $\newline$ The final simplified expression is $49y^{12}$ .

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