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Which expression is equivalent to $(3^2)^1$ ? $\newline$ Choices: $\newline$ (A) $3^3$ $\newline$ (B) $\frac{1}{3^3}$ $\newline$ (C) $\frac{1}{3^2}$ $\newline$ (D) $3^2$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(3^2)^1

?

\newline

Choices:

\newline

(A)

3^3

\newline

(B)

\frac{1}{3^3}

\newline

(C)

\frac{1}{3^2}

\newline

(D)

3^2

Simplify Exponent: Simplify the expression $(3^2)^1$ . When an exponent is raised to another exponent, we multiply the exponents. $(3^2)^1 = 3^{(2*1)} = 3^2$
Check Choices: Check the choices to find the equivalent expression. $\newline$ (A) $3^3$ is not equivalent because it would be $3*3*3$ . $\newline$ (B) $\frac{1}{3^3}$ is not equivalent because it represents the reciprocal of $3^3$ . $\newline$ (C) $\frac{1}{3^2}$ is not equivalent because it represents the reciprocal of $3^2$ . $\newline$ (D) $3^2$ is equivalent because it matches the simplified expression from Step $1$ .

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