Evaluate (-125)^(1/3)

Problem

(−125)(1/3)

Solution

1. Identify the operation as finding the cube root of a negative number.

2. Rewrite the expression using radical notation to visualize the cube root.

√(3,−125)

3. Factor the number inside the radical to find a value that, when multiplied by itself three times, equals −125

−125=(−5)⋅(−5)⋅(−5)

4. Simplify the expression by extracting the base of the cube.

√(3,(−5)3)=−5

Final Answer

(−125)(1/3)=−5

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