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Simplify. Express your answer using a single exponent. $\newline$ $(10d^2)^3$

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Powers of a power: variable bases

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

\newline

(10d^2)^3

Apply Power Separately: Apply the power to both the coefficient and the variable separately. $\newline$ When raising a power to a power, we multiply the exponents, and when raising a coefficient to a power, we simply calculate the power of the number. $\newline$ $(10d^2)^3 = 10^3 \times (d^2)^3$
Calculate $10^3$ : Calculate $10^3$ . $\newline$ $10^3 = 10 \times 10 \times 10 = 1000$
Calculate $(d^2)^3$ : Calculate $(d^2)^3$ . When raising a power to another power, we multiply the exponents. $(d^2)^3 = d^{(2 \times 3)} = d^6$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(10d^2)^3 = 10^3 \times (d^2)^3 = 1000 \times d^6$
Write Final Expression: Write the final simplified expression. $\newline$ The expression $(10d^2)^3$ simplifies to $1000d^6$ .

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