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Which two expressions are equivalent to each other? $\newline$ Multi-select Choices: $\newline$ (A) $10^{10} \times 10^{-3}$ $\newline$ (B) $\frac{1}{10^{7}}$ $\newline$ (C) $\frac{1}{10^{-3}}$ $\newline$ (D) $\frac{10^{7}}{10^{4}}$

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Simplify exponential expressions using exponent rules

Full solution

Q. Which two expressions are equivalent to each other?

\newline

Multi-select Choices:

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(A)

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

\newline

(B)

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

\newline

(C)

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

\newline

(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 $10^3$ .

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