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Simplify. Express your answer using a single exponent. $\newline$ $(10u^2)^2$

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Powers of a power: variable bases

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

\newline

(10u^2)^2

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that when raising a power to another power, you multiply the exponents. For the expression $(10u^2)^2$ , we will apply this rule to both the numerical coefficient and the variable. $\newline$ $(10u^2)^2 = 10^2 \times (u^2)^2$
Calculate $10^2$ : Calculate $10^2$ . $\newline$ $10^2$ means $10$ multiplied by itself, which equals $100$ . $\newline$ $10^2 = 100$
Calculate $(u^2)^2$ : Calculate $(u^2)^2$ . Using the power of a power rule, we multiply the exponents. Since the base is $u$ and the exponents are both $2$ , we get: $(u^2)^2 = u^{(2 \times 2)} = u^4$
Combine Results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to get the final simplified expression. $\newline$ $(10u^2)^2 = 100 \times u^4$

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