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

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Powers of a power: variable bases

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

\newline

(9b^2)^2

Apply power rule: Apply the power of a power rule to \(9b^ $2$ )^ $2$ \. The power of a power rule states that a^n)^m = a^{n*m}\. We will apply this rule to both the numerical part and the variable part of the expression. \(\(9b^ $2$ )^ $2$ = $9$ ^ $2$ * (b^ $2$ )^ $2$ \
Calculate $9^2$ : Calculate $9^2$ . $\newline$ $9^2 = 9 \times 9 = 81$
Calculate $(b^2)^2$ : Calculate $(b^2)^2$ using the power of a power rule. $\newline$ $(b^2)^2 = b^{(2*2)} = b^4$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(9b^2)^2 = 81 \times b^4$
Write final expression: Write the final simplified expression. $\newline$ The expression $(9b^2)^2$ simplifies to $81b^4$ .

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