Select all the expressions that are equivalent to 10^3 * 10^-2. Multi-select Choices: (A)1/10^-6 (B)1/10 (C)10^-6 (D)10

Simplify Expression: Simplify the expression 10^3 * 10^-2. When multiplying powers with the same base, we add the exponents. 10^3 * 10^-2 = 10^(3 + (-2)) = 10^1 = 10Compare to Choices: Compare the simplified expression to the choices. 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) 1/10^-6. 1/10^-6 is equivalent to 10^6, which is not equal to 10.Check Choice (B): Check choice (B) 1/10. 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.

Home

Math Problems

Algebra 1

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.