help please :)

Question

Simplify these expressions:

 

A) √{(27xy^5)/(12x^5 y^3)}

 

B) 3√{(x^5 y^-2)/(8x^2y^2)}

 

C) {(2x^1/2)/(y^1/3)}^-6

 

D) (-27x^9)^1/3

Answer 1

A) √{(27xy⁵)/(12x⁵ y³)}

=√{(3.3.3.x.y². y³)/(3.2.2.x².x².x.y³)}

=√{(3.3.y.y)/(2.2.x².x²)}

=3y/2x²

 

B) ₃√{(x⁵ y^-2)/(8x²y²)}

=₃√{(x³.x²)/(2.2.2.x².y.y.y²)}

=₃√{(x³)/2³.y.y³)}

=x/(2y.₃√y)

=x/(2y.y^1/3)

=xy^-1/3/2y

 

 

C) {(2x^1/2)/(y^1/3)}^-6

={(2^-6. 3x^1/2.(-6))/(y^1/3.(-6))

={(2^-6. x^1/2.(-3).2)/(y^1/3.(-2).3)

={(2^-6. x^-3)/(y^-2)

=y²/2⁶x³

=y²/64x³

 

 

D) (-27x⁹)^1/3
=(-[3.3.3]x⁹)^1/3
=(-3³.x⁹)^1/3

=-(3^3.1/3.x^3.3.1/3)

=-3x³