Evaluate 16^(1/4)

Problem

16(1/4)

Solution

1. Identify the meaning of the fractional exponent. An exponent of 1/4 represents the fourth root of the base.

16(1/4)=√(4,16)

2. Rewrite the base as a power of a smaller integer. We look for a number that, when multiplied by itself four times, equals 16

16=2⋅2⋅2⋅2

16=2

3. Substitute the power back into the expression and apply the power of a power rule, which states (am)n=a(m⋅n)

(2)(1/4)=2(4⋅1/4)

4. Simplify the exponent by performing the multiplication.

4⋅1/4=1

2=2

Final Answer

16(1/4)=2

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