Simplify square root of x^13

Problem

√(,x13)

Solution

1. Rewrite the expression using a fractional exponent.

√(,x13)=(x13)1/2

2. Apply the power of a power rule by multiplying the exponents.

(x13)1/2=x13/2

3. Decompose the exponent into an integer part and a fractional part to simplify the radical.

x13/2=x(6+1/2)

4. Separate the terms using the product rule for exponents.

x(6+1/2)=x6⋅x1/2

5. Convert the fractional exponent back into radical form.

x6⋅x1/2=x6√(,x)

Final Answer

√(,x13)=x6√(,x)

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