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

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Powers of a power: variable bases

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

\newline

(5d^2)^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 $(5d^2)^2$ , which means we need to apply the exponent of $2$ to both $5$ and $d^2$ . $\newline$ $(5d^2)^2 = 5^2 \times (d^2)^2$
Calculate $5^2$ : Calculate $5^2$ . $\newline$ $5^2$ means $5$ multiplied by itself, which is $25$ . $\newline$ $5^2 = 25$
Calculate $(d^2)^2$ : Calculate $(d^2)^2$ . Using the power to a power rule, we multiply the exponents $2$ and $2$ . $(d^2)^2 = d^{(2*2)} = d^4$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ Now we combine the results to express the simplified form of the original expression. $\newline$ $(5d^2)^2 = 5^2 \times d^4 = 25d^4$

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