Simplify

Problem

√(,125*x5*y6)/√(,5*x3*y10)

Solution

1. Apply the quotient property of radicals to combine the two square roots into a single radical expression.

√(,(125*x5*y6)/(5*x3*y10))

2. Simplify the fraction inside the radical by dividing the coefficients and applying the laws of exponents for the variables.

125/5=25

(x5)/(x3)=x(5−3)=x2

(y6)/(y10)=y(6−10)=y(−4)

3. Rewrite the expression inside the radical using the simplified terms.

√(,25*x2*y(−4))

4. Take the square root of each factor individually.

√(,25)⋅√(,x2)⋅√(,y(−4))

5⋅x⋅y(−2)

5. Express with positive exponents by moving the variable with the negative exponent to the denominator.

(5*x)/(y2)

Final Answer

√(,125*x5*y6)/√(,5*x3*y10)=(5*x)/(y2)

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