Evaluate fourth root of (-7)^4

Problem

√(4,(−7)4)

Solution

1. Evaluate the expression inside the radical by raising −7 to the fourth power.

(−7)4=(−7)⋅(−7)⋅(−7)⋅(−7)

(−7)4=2401

2. Apply the definition of the principal nth root, where √(n,xn)=|x| when n is even.

√(4,2401)=|−7|

3. Simplify the absolute value to find the positive root.

|−7|=7

Final Answer

√(4,(−7)4)=7

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