Evaluate 125^(-1/3)

Problem

125(−1/3)

Solution

1. Apply the negative exponent rule by rewriting the expression as a reciprocal with a positive exponent.

125(−1/3)=1/(125(1/3))

2. Convert the rational exponent to radical form, where the power of 1/3 represents a cube root.

1/(125(1/3))=1/√(3,125)

3. Evaluate the cube root by identifying the number that, when multiplied by itself three times, equals 125

5×5×5=125

√(3,125)=5

4. Substitute the value back into the fraction to find the final result.

1/5

Final Answer

125(−1/3)=1/5

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