Evaluate (1/27)^(2/3)

Problem

(1/27)2/3

Solution

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

(1/27)2/3=1/27

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

1=1

3. Rewrite the denominator using the property am/n=(√(n,a))m

27=(√(3,27))2

4. Evaluate the cube root of 27.

√(3,27)=3

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

3=9

6. Combine the results into the final fraction.

1/9

Final Answer

(1/27)2/3=1/9

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