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Simplify. Express your answer using a single exponent. $\newline$ $(9x^4)^2$

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Powers of a power: variable bases

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

\newline

(9x^4)^2

Apply Power Rule: Apply the power of a power rule to the expression $(9x^4)^2$ . The power of a power rule states that $(a^m)^n = a^{m*n}$ . Therefore, we need to apply the exponent of $2$ to both the base $9$ and the exponent of $x^4$ . $(9x^4)^2 = 9^2 \times (x^4)^2$
Calculate $9^2$ : Calculate $9^2$ . $\newline$ $9^2 = 9 \times 9 = 81$
Calculate $(x^4)^2$ : Calculate $(x^4)^2$ . Using the power of a power rule, we multiply the exponents. $(x^4)^2 = x^{(4*2)} = x^8$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $81$ from $9^2$ and $x^8$ from $(x^4)^2$ , so we combine them to get the final simplified expression. $\newline$ $(9x^4)^2 = 81x^8$

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