Evaluate (1/125)^(2/3)

Problem

(1/125)2/3

Solution

1. Apply the power of a quotient rule by distributing the exponent to both the numerator and the denominator.

(1/125)2/3=1/125

2. Simplify the numerator since 1 raised to any power is 1.

1/125

3. Rewrite the denominator using the definition of rational exponents, where am/n=(√(n,a))m

1/((√(3,125))2)

4. Evaluate the cube root of 125, which is 5 because 5×5×5=125

1/5

5. Square the result to find the final value.

1/25

Final Answer

(1/125)2/3=1/25

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