Evaluate sixth root of 1/64

Problem

√(6,1/64)

Solution

1. Rewrite the expression using the property of radicals that allows the root to be applied to the numerator and denominator separately.

√(6,1/64)=√(6,1)/√(6,64)

2. Evaluate the sixth root of the numerator, noting that any root of 1 is 1.

√(6,1)=1

3. Identify the sixth root of the denominator by expressing 64 as a power of a prime number.

2=64

4. Simplify the denominator using the definition of a root.

√(6,64)=2

5. Combine the results to find the final value.

1/2

Final Answer

√(6,1/64)=1/2

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