Evaluate fourth root of (-2)^4

Problem

√(4,(−2)4)

Solution

1. Evaluate the expression inside the parentheses by raising −2 to the fourth power.

(−2)4=16

2. Substitute the result back into the radical expression.

√(4,16)

3. Find the principal fourth root of 16 which is the positive number that, when multiplied by itself four times, equals 16

2⋅2⋅2⋅2=16

4. Conclude that the fourth root of 16 is 2

√(4,16)=2

Final Answer

√(4,(−2)4)=2

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