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What could be the value of $x$ in the following equation? Select all that apply. $\newline$ $x^3 = \frac{1}{125}$ $\newline$ Multi-select Choices: $\newline$ (A) $-\sqrt[3]{\frac{1}{125}}$ $\newline$ (B) $-\frac{1}{5}$ $\newline$ (C) $\frac{1}{5}$ $\newline$ (D) $\sqrt[3]{\frac{1}{125}}$

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Evaluate integers raised to rational exponents

Full solution

Q. What could be the value of

x

in the following equation? Select all that apply.

\newline

x^3 = \frac{1}{125}

\newline

Multi-select Choices:

\newline

(A)

-\sqrt[3]{\frac{1}{125}}

\newline

(B)

-\frac{1}{5}

\newline

(C)

\frac{1}{5}

\newline

(D)

\sqrt[3]{\frac{1}{125}}

Identify Equation: Identify the equation and what it asks. $\newline$ $x^3 = \frac{1}{125}$ $\newline$ We need to find $x$ such that when cubed, it equals $\frac{1}{125}$ .
Simplify Right Side: Simplify the right side of the equation. $\newline$ $\frac{1}{125}$ can be written as $\left(\frac{1}{5}\right)^3$ because $5^3 = 125$ . $\newline$ $x^3 = \left(\frac{1}{5}\right)^3$
Apply Cube Root: Apply the cube root to both sides. $\newline$ Taking the cube root on both sides, we get: $\newline$ $x = \frac{1}{5}$
Check Other Solutions: Check for other possible solutions. $\newline$ Since cubing a negative number also results in a negative number, consider: $\newline$ $x = -\frac{1}{5}$ $\newline$ $(-\frac{1}{5})^3 = -\frac{1}{125}$ , which is not equal to $\frac{1}{125}$ .

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