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Select all the expressions that are equivalent to $\frac{9^{36}}{9^{-4}}$ . $\newline$ Multi-select Choices: $\newline$ (A) $9^{-40}$ $\newline$ (B) $9^{-9}$ $\newline$ (C) $\frac{1}{9^{-40}}$ $\newline$ (D) $\frac{1}{9^{-9}}$

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Identify equivalent exponential expressions II

Full solution

Q. Select all the expressions that are equivalent to

\frac{9^{36}}{9^{-4}}

.

\newline

Multi-select Choices:

\newline

(A)

9^{-40}

\newline

(B)

9^{-9}

\newline

(C)

\frac{1}{9^{-40}}

\newline

(D)

\frac{1}{9^{-9}}

Understand operation with exponents: Understand the operation to perform with the exponents. $\newline$ When dividing powers with the same base, we subtract the exponents according to the rule $\frac{a^m}{a^n} = a^{(m-n)}$ .
Calculate result of $\frac{9^{36}}{9^{-4}}$ : Calculate the result of $\frac{9^{36}}{9^{-4}}$ by subtracting the exponents. $\newline$ $\frac{9^{36}}{9^{-4}} = 9^{(36 - (-4))} = 9^{(36 + 4)} = 9^{40}$
Determine equivalence of given choices: Determine if the given choices are equivalent to $9^{40}$ . $\newline$ - $9^{-40}$ is not equivalent because it represents $\frac{1}{9^{40}}$ . $\newline$ - $9^{-9}$ is not equivalent because it represents $\frac{1}{9^{9}}$ . $\newline$ - $\frac{1}{9^{-40}}$ is equivalent because it represents $9^{40}$ . $\newline$ - $\frac{1}{9^{-9}}$ is not equivalent because it represents $9^{9}$ .

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