Select all the expressions that are equivalent to 9^-7 * 9^-1. Multi-select Choices: (A)1/9^8 (B)1/9^-8 (C)9^-8 (D)9^7

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

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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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Math Problems

Algebra 1

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)