Select all the expressions that are equivalent to (8^-3)^1. Multi-select Choices: (A)1/8^3 (B)1/8^-3 (C)8^-2 (D)1/8^-2

Understand the expression: Understand the expression (8^-3)^1. The expression (8^-3)^1 means that we have 8 raised to the power of -3, and then this result is raised to the power of 1. Raising any number to the power of 1 leaves the number unchanged. (8^-3)^1 = 8^-3Compare with given choices: Compare the expression 8^-3 to the choices given. We need to determine which of the given choices are equivalent to 8^-3. (A) 1/8^3 is equivalent to 8^-3 because a negative exponent indicates the reciprocal of the base raised to the positive exponent. 8^-3 = 1/8^3

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

(8^{-3})^1

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Multi-select Choices:

\newline

(A)

\frac{1}{8^3}

\newline

(B)

\frac{1}{8^{-3}}

\newline

(C)

8^{-2}

\newline

(D)

\frac{1}{8^{-2}}

Understand the expression: Understand the expression $(8^{-3})^1$ . $\newline$ The expression $(8^{-3})^1$ means that we have $8$ raised to the power of $-3$ , and then this result is raised to the power of $1$ . Raising any number to the power of $1$ leaves the number unchanged. $\newline$ $(8^{-3})^1 = 8^{-3}$
Compare with given choices: Compare the expression $8^{-3}$ to the choices given. $\newline$ We need to determine which of the given choices are equivalent to $8^{-3}$ . $\newline$ (A) $\frac{1}{8^3}$ is equivalent to $8^{-3}$ because a negative exponent indicates the reciprocal of the base raised to the positive exponent. $\newline$ $8^{-3} = \frac{1}{8^3}$