Evaluate fourth root of 4

Problem

√(4,4)

Solution

1. Rewrite the expression using a fractional exponent.

√(4,4)=4(1/4)

2. Express the base as a power of 2.

4=2

3. Substitute the power into the expression.

(2)(1/4)

4. Apply the power of a power rule by multiplying the exponents.

2(2⋅1/4)=2(2/4)

5. Simplify the fraction in the exponent.

2(1/2)

6. Convert the fractional exponent back into radical form.

2(1/2)=√(,2)

Final Answer

√(4,4)=√(,2)

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