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Which expression is equivalent to $(9^2)^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{9^8}$ $\newline$ (B) $9^{12}$ $\newline$ (C) $\frac{1}{9^{12}}$ $\newline$ (D) $9^8$

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Identify equivalent exponential expressions I

Full solution

Q. Which expression is equivalent to

(9^2)^6

?

\newline

Choices:

\newline

(A)

\frac{1}{9^8}

\newline

(B)

9^{12}

\newline

(C)

\frac{1}{9^{12}}

\newline

(D)

9^8

Simplify Expression: Step $1$ : Simplify the expression using the power of a power rule. $\newline$ $(9^2)^6$ means we raise $9$ to the power of $2$ , and then raise the result to the power of $6$ . $\newline$ Using the rule $(a^m)^n = a^{m*n}$ , we calculate: $\newline$ $(9^2)^6 = 9^{2*6} = 9^{12}$ .
Calculate Result: Step $2$ : Match the result with the given choices. $\newline$ We found that $(9^2)^6$ simplifies to $9^{12}$ . $\newline$ Checking the choices: $\newline$ (A) $\frac{1}{9^8}$ $\newline$ (B) $9^{12}$ $\newline$ (C) $\frac{1}{9^{12}}$ $\newline$ (D) $9^8$ $\newline$ Choice (B) $9^{12}$ matches our calculation.

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