Evaluate 256^(1/4)

Problem

256(1/4)

Solution

1. Identify the operation as finding the fourth root of the number 256

2. Rewrite the base 256 as a power of a smaller integer to simplify the radical.

3. Recognize that 256 is a power of 2 or 4 Specifically, 4×4×4×4=256

4. Substitute 4 for 256 into the expression.

(4)(1/4)

5. Apply the power of a power rule, which states (am)n=a(m⋅n)

4(4⋅1/4)

6. Simplify the exponent by multiplying 4 and 1/4

4=4

Final Answer

256(1/4)=4

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