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Which expression is equivalent to $9^9 \times 9^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{9^{15}}$ $\newline$ (B) $\frac{1}{9^{54}}$ $\newline$ (C) $9^{54}$ $\newline$ (D) $9^{15}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

9^9 \times 9^6

?

\newline

Choices:

\newline

(A)

\frac{1}{9^{15}}

\newline

(B)

\frac{1}{9^{54}}

\newline

(C)

9^{54}

\newline

(D)

9^{15}

Combine exponents: Step $1$ : Combine the exponents of the same base. $\newline$ $9^9 \times 9^6$ can be rewritten by adding the exponents since the base is the same. $\newline$ Calculation: $9^{(9+6)} = 9^{15}$
Match with choices: Step $2$ : Match the result with the given choices. $\newline$ We have $9^{15}$ from Step $1$ . $\newline$ Choices are: $\newline$ (A) $\frac{1}{9^{15}}$ $\newline$ (B) $\frac{1}{9^{54}}$ $\newline$ (C) $9^{54}$ $\newline$ (D) $9^{15}$

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