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Simplify. Express your answer using a single exponent. $\newline$ $(7u^5)^2$

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Powers of a power: variable bases

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

\newline

(7u^5)^2

Apply Power Rule: Apply the power to a power rule. $\newline$ When raising a power to another power, we multiply the exponents. For the expression $(7u^5)^2$ , we apply this rule to the variable $u$ . $\newline$ $(7u^5)^2 = 7^2 \times (u^5)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ $7^2$ is $7$ multiplied by itself. $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(u^5)^2$ : Calculate $(u^5)^2$ . We multiply the exponents for $u$ . $(u^5)^2 = u^{(5 \times 2)} = u^{10}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $7^2 = 49$ and $(u^5)^2 = u^{10}$ . Now we combine these to express the simplified form of the original expression. $\newline$ $(7u^5)^2 = 49u^{10}$

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