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Simplify. Express your answer using a single exponent. $\newline$ $(7u^9)^2$

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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^9)^2

Apply Power Rule: Apply the power of a power rule to $(7u^9)^2$ . The power of a power rule states that $(a^m)^n = a^{m*n}$ . Therefore, we need to apply the exponent outside the parentheses to both the base number $7$ and the variable $u$ raised to the $9$ th power. $(7u^9)^2 = 7^2 \times (u^9)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ $7^2$ is $7$ multiplied by itself. $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(u^9)^2$ : Calculate $(u^9)^2$ . Using the power of a power rule, we multiply the exponents. $(u^9)^2 = u^{(9*2)} = u^{18}$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $7^2 = 49$ and $(u^9)^2 = u^{18}$ . Now we combine these to express the answer using a single exponent. $\newline$ $(7u^9)^2 = 49u^{18}$

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