Find the Domain sixth root of x^6

Problem

√(6,x6)

Solution

1. Identify the function as ƒ(x)=√(6,x6) which involves an even root of a variable raised to an even power.

2. Determine the restriction for an even root, which requires the radicand (the expression inside the root) to be non-negative: x6≥0

3. Analyze the inequality x6≥0 Since any real number raised to an even power is always greater than or equal to zero, this condition is satisfied for all real numbers.

4. Conclude that there are no values of x that make the expression undefined.

Final Answer

Domain of √(6,x6)=(−∞,∞)

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