Simplify fourth root of x^12

Problem

√(4,x12)

Solution

1. Identify the radical expression and rewrite it using a fractional exponent.

2. Apply the rule for radicals where √(n,am)=am/n

3. Substitute the given values n=4 and m=12 into the exponent.

x12/4

4. Simplify the fraction in the exponent by dividing 12 by 4.

x3

5. Consider the absolute value if x could be negative, but since the resulting power 3 is odd and the original index 4 is even, the standard simplification for real numbers assumes the principal root.

Final Answer

√(4,x12)=x3

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