Evaluate fourth root of (-3)^4

Problem

√(4,(−3)4)

Solution

1. Evaluate the expression inside the radical by raising −3 to the fourth power.

(−3)4=(−3)⋅(−3)⋅(−3)⋅(−3)

(−3)4=81

2. Substitute the result back into the radical expression.

√(4,81)

3. Find the principal fourth root of 81 which is the positive number that, when multiplied by itself four times, equals 81

3⋅3⋅3⋅3=81

√(4,81)=3

Final Answer

√(4,(−3)4)=3

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