Simplify square root of x^19

Problem

√(,x19)

Solution

1. Rewrite the expression using a fractional exponent to represent the square root.

√(,x19)=(x19)(1/2)

2. Apply the power of a power rule, which states that (am)n=a(m⋅n)

(x19)(1/2)=x(19/2)

3. Decompose the exponent into an integer and a fraction to separate the perfect square part.

x(19/2)=x(18/2+1/2)

4. Simplify the exponents using the product rule a(m+n)=am⋅an

x(18/2)⋅x(1/2)=x9⋅x(1/2)

5. Convert the fractional exponent back into radical form.

x9√(,x)

Final Answer

√(,x19)=x9√(,x)

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