Evaluate (1/256)^(1/4)

Problem

(1/256)1/4

Solution

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

(1/256)1/4=1/256

2. Simplify the numerator by recognizing that any positive power of 1 is 1

1=1

3. Rewrite the denominator by expressing 256 as a power of a smaller integer to find its fourth root.

256=4

4. Evaluate the fourth root of the denominator using the property (an)1/n=a

256=(4)1/4=4

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

1/4

Final Answer

(1/256)1/4=1/4

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