Evaluate (-125)^(2/3)

Problem

(−125)(2/3)

Solution

1. Rewrite the expression using the property of rational exponents a(m/n)=(√(n,a))m

(−125)(2/3)=(√(3,−125))2

2. Evaluate the cube root of −125 Since (−5)×(−5)×(−5)=−125 the cube root is −5

√(3,−125)=−5

3. Square the result of the cube root.

(−5)2=25

Final Answer

(−125)(2/3)=25

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