Evaluate (1/81)^(3/4)

Problem

(1/81)3/4

Solution

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

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

2. Simplify the numerator since any positive power of 1 is equal to 1

1/81

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

1/((√(4,81))3)

4. Evaluate the fourth root of 81 by identifying that 3=81

1/((3)3)

5. Calculate the cube of 3 to find the final value.

1/27

Final Answer

(1/81)3/4=1/27

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