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Which expression is equivalent to $3^9 \times 3^2$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{3^{11}}$ $\newline$ (B) $\frac{1}{3^{18}}$ $\newline$ (C) $3^{11}$ $\newline$ (D) $3^{18}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

3^9 \times 3^2

?

\newline

Choices:

\newline

(A)

\frac{1}{3^{11}}

\newline

(B)

\frac{1}{3^{18}}

\newline

(C)

3^{11}

\newline

(D)

3^{18}

Identify Base and Exponents: Step $1$ : Identify the base and the exponents in the expression $3^9 \times 3^2$ . $\newline$ Base: $3$ $\newline$ Exponents: $9, 2$
Combine Exponents: Step $2$ : Combine the exponents since the base is the same. $\newline$ $3^9 \times 3^2 = 3^{(9+2)} = 3^{11}$
Check Choices: Step $3$ : Check the choices to find the equivalent expression. $\newline$ Choices are: $\newline$ (A) $\frac{1}{3^{11}}$ $\newline$ (B) $\frac{1}{3^{18}}$ $\newline$ (C) $3^{11}$ $\newline$ (D) $3^{18}$ $\newline$ Correct choice is (C) $3^{11}$ .

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