Evaluate (1/81)^(1/4)

Problem

(1/81)1/4

Solution

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

(1/81)1/4=1/81

2. Evaluate the numerator by finding the fourth root of 1.

1=1

3. Evaluate the denominator by finding the fourth root of 81, noting that 3=81

81=3

4. Combine the results to find the final value of the fraction.

1/3

Final Answer

(1/81)1/4=1/3

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