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

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Powers of a power: variable bases

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

\newline

(9g^{9})^{2}

Apply power rule: Apply the power of a power rule to the expression $(9g^9)^2$ . $\newline$ The power of a power rule states that when raising a power to another power, you multiply the exponents. For the coefficient $9$ , which is also raised to the power of $2$ , we simply square it. $\newline$ $(9g^9)^2 = 9^2 \times (g^9)^2$
Calculate $9^2$ : Calculate $9^2$ . $\newline$ $9^2 = 9 \times 9 = 81$
Calculate $(g^9)^2$ : Calculate $(g^9)^2$ . Using the power of a power rule, we multiply the exponents. $(g^9)^2 = g^{(9 \times 2)} = g^{18}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $81$ for $9^2$ and $g^{18}$ for $(g^9)^2$ , so we combine them to get the final simplified expression. $\newline$ $(9g^9)^2 = 81g^{18}$

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