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Which expression is equivalent to $6^2 \times 6^9$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{6^{18}}$ $\newline$ (B) $6^{18}$ $\newline$ (C) $6^{11}$ $\newline$ (D) $\frac{1}{6^{11}}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

6^2 \times 6^9

?

\newline

Choices:

\newline

(A)

\frac{1}{6^{18}}

\newline

(B)

6^{18}

\newline

(C)

6^{11}

\newline

(D)

\frac{1}{6^{11}}

Identify Base and Exponents: Identify the base and the exponents. $\newline$ In $6^2$ and $6^9$ , $6$ is the base raised to the exponents $2$ and $9$ respectively. $\newline$ Base: $6$ $\newline$ Exponents: $2$ , $9$
Rewrite as Single Power: Given expression: $6^2 \times 6^9$ $\newline$ Rewrite this expression as a single power of $6$ . $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $6^2 \times 6^9$ $\newline$ $= 6^{2+9}$ $\newline$ $= 6^{11}$
Choose Equivalent Expression: Choose the equivalent expression for $6^2 \times 6^9$ . From the calculation in Step $2$ , we have determined that $6^2 \times 6^9$ is equal to $6^{11}$ . Therefore, the equivalent expression is $6^{11}$ .

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