Select all the expressions that are equivalent to (10^3)^1. Multi-select Choices: (A)1/10^4 (B)10^3 (C)10^4 (D)1/10^3

Evaluate Expression: Evaluate the expression (10^3)^1 using the power of a power rule. The power of a power rule states that (a^m)^n = a^(m*n). Therefore, (10^3)^1 = 10^(3*1) = 10^3.Compare Choices: Compare the evaluated expression 10^3 with the given choices. (A) 1/10^4 is not equivalent to 10^3 because it represents the reciprocal of 10^4. (B) 10^3 is equivalent to 10^3 by definition. (C) 10^4 is not equivalent to 10^3 because it represents 10 raised to the power of 4, not 3. (D) 1/10^3 is not equivalent to 10^3 because it represents the reciprocal of 10^3.Select Correct Choice: Select the correct choices based on the comparison. The only expression equivalent to (10^3)^1 is 10^3. Therefore, the correct choice is (B) 10^3.

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Calculus

Find derivatives of using multiple formulae

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Q. Select all the expressions that are equivalent to

(10^3)^1

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{10^4}

\newline

(B)

10^3

\newline

(C)

10^4

\newline

(D)

\frac{1}{10^3}

Evaluate Expression: Evaluate the expression $(10^3)^1$ using the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . $\newline$ Therefore, $(10^3)^1 = 10^{3*1} = 10^3$ .
Compare Choices: Compare the evaluated expression $10^3$ with the given choices. $\newline$ (A) $\frac{1}{10^4}$ is not equivalent to $10^3$ because it represents the reciprocal of $10^4$ . $\newline$ (B) $10^3$ is equivalent to $10^3$ by definition. $\newline$ (C) $10^4$ is not equivalent to $10^3$ because it represents $10$ raised to the power of $4$ , not $\frac{1}{10^4}$ $0$ . $\newline$ (D) $\frac{1}{10^4}$ $1$ is not equivalent to $10^3$ because it represents the reciprocal of $10^3$ .
Select Correct Choice: Select the correct choices based on the comparison. $\newline$ The only expression equivalent to $(10^3)^1$ is $10^3$ . $\newline$ Therefore, the correct choice is (B) $10^3$ .