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

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

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

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{9^8}

\newline

(B)

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

\newline

(C)

9^{-9}

\newline

(D)

9^8

Simplify Expression: Step $1$ : Simplify the expression $9^{-1} \times 9^{-8}$ . We know that when multiplying powers with the same base, we add the exponents. Calculation: $9^{-1} \times 9^{-8} = 9^{(-1 + -8)} = 9^{-9}$
Compare to Choices: Step $2$ : Compare the simplified expression to the given choices. $\newline$ We need to find which choices are equivalent to $9^{-9}$ . $\newline$ (A) $\frac{1}{9^8} = 9^{-8}$ (not equal to $9^{-9}$ ) $\newline$ (B) $\frac{1}{9^{-9}} = 9^9$ (not equal to $9^{-9}$ ) $\newline$ (C) $9^{-9}$ (this is exactly $9^{-9}$ ) $\newline$ (D) $9^8 = 9^8$ (not equal to $9^{-9}$ )

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