Evaluate (1/8)^(2/3)

Problem

(1/8)2/3

Solution

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

(1/8)2/3=1/8

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

1=1

3. Rewrite the denominator using the property am/n=(√(n,a))m to express the fractional exponent as a radical.

8=(√(3,8))2

4. Evaluate the cube root of 8.

√(3,8)=2

5. Square the result to find the final value of the denominator.

2=4

6. Combine the results into the final fraction.

1/4

Final Answer

(1/8)2/3=1/4

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