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Select all the expressions that are equivalent to $10^3 \times 10^{-2}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{10^{-6}}$ $\newline$ (B) $\frac{1}{10}$ $\newline$ (C) $10^{-6}$ $\newline$ (D) $10$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

10^3 \times 10^{-2}

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{10^{-6}}

\newline

(B)

\frac{1}{10}

\newline

(C)

10^{-6}

\newline

(D)

10

Simplify Expression: Simplify the expression $10^3 \times 10^{-2}$ . $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $10^3 \times 10^{-2} = 10^{3 + (-2)} = 10^1 = 10$
Compare to Choices: Compare the simplified expression to the choices. $\newline$ We have simplified the expression to $10$ , which is $10^1$ . Now we need to check which of the given choices are equivalent to $10$ .
Check Choice (A): Check choice (A) $\frac{1}{10^{-6}}$ . $\frac{1}{10^{-6}}$ is equivalent to $10^6$ , which is not equal to $10$ .
Check Choice (B): Check choice (B) $\frac{1}{10}$ . $\frac{1}{10}$ is equivalent to $10^{-1}$ , which is not equal to $10$ .
Check Choice (C): Check choice (C) $10^{-6}$ . $10^{-6}$ is not equal to $10$ .
Check Choice (D): Check choice (D) $10$ . $10$ is equal to $10$ , which matches our simplified expression.

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