Evaluate fourth root of (-5)^4

Problem

√(4,(−5)4)

Solution

1. Evaluate the expression inside the radical by raising −5 to the fourth power.

(−5)4=(−5)⋅(−5)⋅(−5)⋅(−5)

(−5)4=625

2. Substitute the result back into the fourth root expression.

√(4,625)

3. Find the principal fourth root of 625 which is the non-negative number that, when multiplied by itself four times, equals 625

5⋅5⋅5⋅5=625

√(4,625)=5

Final Answer

√(4,(−5)4)=5

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