Question

Simplify the following:

`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`

Answer 1

`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`

= `(x^4y^2)^(1/3) ÷ (x^5y^-5)^(1/6)`

= `(x^(4xx1/3)y^(2xx1/3)) ÷ (x^(5xx1/6)y^(-5xx1/6))`    .....(Using (a^m)ⁿ = a^mn)

= `(x^(4/3)y^(2/3)) ÷ (x^(5/6)y^(-5/6))`

= `(x^(4/3)y^(2/3))/(x^(5/6)y^(-5/6))`

= `x^(4/3 - 5/6)y^(2/3 - (-5/6)`  .....(Using (a^m)ⁿ = a^mn)

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

= `x^(1/2)(y^3)^(1/2)`     .....(Using (a^m)ⁿ = a^mn)

= `sqrt(x) sqrt(y^3)`

= `sqrt(xy^3)`.