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Simplify. Express your answer using a single exponent. $\newline$ $(5r^6)^2$

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Powers of a power: variable bases

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

\newline

(5r^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 $(5r^6)^2$ , which means we need to apply the exponent of $2$ to both $5$ and $r^6$ . $\newline$ $(5r^6)^2 = 5^2 \times (r^6)^2$
Calculate $5^2$ : Calculate $5^2$ . $\newline$ $5^2$ means $5$ multiplied by itself, which is $25$ . $\newline$ $5^2 = 25$
Calculate $(r^6)^2$ : Calculate $(r^6)^2$ . Using the power to a power rule, we multiply the exponents $6$ and $2$ . $(r^6)^2 = r^{(6*2)} = r^{12}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $5^2 = 25$ and $(r^6)^2 = r^{12}$ . Now we combine these to express the simplified form of the original expression. $\newline$ $(5r^6)^2 = 25 \times r^{12}$

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