Evaluate 125^(-2/3)

Problem

125(−2/3)

Solution

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

125(−2/3)=1/(125(2/3))

2. Rewrite the rational exponent using the property a(m/n)=(√(n,a))m

1/(125(2/3))=1/((√(3,125))2)

3. Evaluate the cube root of 125, noting that 5×5×5=125

1/((√(3,125))2)=1/5

4. Square the result to find the final value.

1/5=1/25

Final Answer

125(−2/3)=1/25

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