Simplify square root of x^6

Problem

√(,x6)

Solution

1. Identify the expression as a square root of a power, which can be rewritten using a fractional exponent.

2. Apply the rule for radicals where √(n,am)=am/n In this case, the index n is 2 and the exponent m is 6

√(,x6)=(x6)1/2

3. Apply the power of a power rule by multiplying the exponents: (am)n=a(m⋅n)

x(6⋅1/2)=x3

4. Consider the absolute value because the index of the root is even and the resulting exponent is odd, ensuring the result is non-negative.

|x3|

Final Answer

√(,x6)=|x3|

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