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Which expression is equivalent to $(7^9)^2$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{7^{18}}$ $\newline$ (B) $7^{11}$ $\newline$ (C) $\frac{1}{7^{11}}$ $\newline$ (D) $7^{18}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(7^9)^2

?

\newline

Choices:

\newline

(A)

\frac{1}{7^{18}}

\newline

(B)

7^{11}

\newline

(C)

\frac{1}{7^{11}}

\newline

(D)

7^{18}

Simplify Power Rule: Simplify the expression $(7^9)^2$ using the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . Therefore, we can simplify $(7^9)^2$ as follows: $\newline$ $(7^9)^2 = 7^{9*2} = 7^{18}$
Match Simplified Expression: Match the simplified expression to the given choices. $\newline$ We have simplified the expression to $7^{18}$ . Now we need to see which of the given choices matches this expression. $\newline$ (A) $\frac{1}{7^{18}}$ is not correct because it represents the reciprocal of $7^{18}$ . $\newline$ (B) $7^{11}$ is not correct because the exponent is $11$ , not $18$ . $\newline$ (C) $\frac{1}{7^{11}}$ is not correct because it represents the reciprocal of $7^{11}$ and the exponent is incorrect. $\newline$ (D) $7^{18}$ is correct because it matches our simplified expression exactly.

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