Which two expressions are equivalent to each other? Multi-select Choices: (A)10^10 * 10^-3 (B)1/10^7 (C)1/10^-3 (D)10^7/10^4

Simplify Choice (A): Simplify each choice to find equivalencies: (A) $10^{10} \times 10^{-3}$ Calculation: $10^{10 + (-3)} = 10^7$Simplify Choice (B): Simplify choice (B): (B) $ \frac{1}{10^7} $ This expression remains as is, no simplification needed.Simplify Choice (C): Simplify choice (C): (C) $ \frac{1}{10^{-3}} $ Calculation: $10^3$ (since $ \frac{1}{10^{-3}} = 10^3$)Simplify Choice (D): Simplify choice (D): (D) $ \frac{10^7}{10^4} $ Calculation: $10^{7-4} = 10^3$Compare Simplified Results: Compare the simplified results: $10^7$ from (A), $ \frac{1}{10^7} $ from (B), $10^3$ from (C) and $10^3$ from (D). Choices (C) and (D) are equivalent as both simplify to $10^3$.

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

Q. Which two expressions are equivalent to each other?

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Multi-select Choices:

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(A)

10^{10} \times 10^{-3}

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(B)

\frac{1}{10^{7}}

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(C)

\frac{1}{10^{-3}}

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(D)

\frac{10^{7}}{10^{4}}

Simplify Choice (A): Simplify each choice to find equivalencies: $\newline$ (A) $10^{10} \times 10^{-3}$ $\newline$ Calculation: $10^{10 + (-3)} = 10^7$
Simplify Choice (B): Simplify choice (B): $\newline$ (B) $\frac{1}{10^7}$ $\newline$ This expression remains as is, no simplification needed.
Simplify Choice (C): Simplify choice (C): $\newline$ (C) $\frac{1}{10^{-3}}$ $\newline$ Calculation: $10^3$ (since $\frac{1}{10^{-3}} = 10^3$ )
Simplify Choice (D): Simplify choice (D): $\newline$ (D) $\frac{10^7}{10^4}$ $\newline$ Calculation: $10^{7-4} = 10^3$
Compare Simplified Results: Compare the simplified results: $\newline$ $10^7$ from (A), $\frac{1}{10^7}$ from (B), $10^3$ from (C) and $10^3$ from (D). $\newline$ Choices (C) and (D) are equivalent as both simplify to $10^3$ .