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

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Powers of a power: variable bases

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

\newline

(10a^2)^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 $(10a^2)^2$ , which means we need to apply the exponent of $2$ to both $10$ and $a^2$ . $\newline$ $(10a^2)^2 = 10^2 \times (a^2)^2$
Calculate $10^2$ : Calculate $10^2$ . $\newline$ $10^2$ means $10$ multiplied by itself, which is $100$ . $\newline$ $10^2 = 100$
Calculate $(a^2)^2$ : Calculate $(a^2)^2$ . Using the power of a power rule, we multiply the exponents $2$ and $2$ . $(a^2)^2 = a^{(2*2)} = a^4$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $10^2 = 100$ and $(a^2)^2 = a^4$ . Now we combine these to express the simplified form of the original expression. $\newline$ $(10a^2)^2 = 100 \times a^4$
Write final answer: Write the final answer. $\newline$ The final simplified expression is $100a^4$ .

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