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Select all the expressions that are equivalent to $9^{-7} \times 9^{-1}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{9^8}$ $\newline$ (B) $\frac{1}{9^{-8}}$ $\newline$ (C) $9^{-8}$ $\newline$ (D) $9^7$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

9^{-7} \times 9^{-1}

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{9^8}

\newline

(B)

\frac{1}{9^{-8}}

\newline

(C)

9^{-8}

\newline

(D)

9^7

Combine Exponents: Step $1$ : Combine the exponents of the same base $9$ . $\newline$ Calculation: $9^{-7} \times 9^{-1} = 9^{(-7 + -1)} = 9^{-8}$
Convert to Fractional Form: Step $2$ : Convert the expression $9^{-8}$ into a fractional form. $\newline$ Calculation: $9^{-8} = \frac{1}{9^8}$
Compare with Choices: Step $3$ : Compare the result with the given choices. $\newline$ Calculation: $\frac{1}{9^8}$ matches choice (A). $\newline$ Check other choices: $\newline$ (B) $\frac{1}{9^{-8}} = 9^8$ (incorrect), $\newline$ (C) $9^{-8}$ matches, $\newline$ (D) $9^7$ (incorrect)

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