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Simplify. Express your answer using a single exponent. $\newline$ $(6u^2)^3$

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Powers of a power: variable bases

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

\newline

(6u^2)^3

Apply Power Rule: Apply the power to a power rule. $\newline$ To simplify the expression $(6u^2)^3$ , we need to apply the power to a power rule, which states that $(a^m)^n = a^{m*n}$ . We will apply this rule to both the numerical coefficient and the variable with its exponent. $\newline$ $(6u^2)^3 = 6^3 \times (u^2)^3$
Calculate Cube of $6$ : Calculate the cube of $6$ . To find $6^3$ , we multiply $6$ by itself three times. $6^3 = 6 \times 6 \times 6 = 216$
Calculate Cube of $u^2$ : Calculate the cube of $u^2$ . To find $(u^2)^3$ , we multiply the exponents according to the power to a power rule. $(u^2)^3 = u^{2*3} = u^6$
Combine Results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to get the final simplified expression. $\newline$ $(6u^2)^3 = 216 \times u^6$

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