root(3)(25x^11)/root(3)(9w^2)3√25x113√9w2
we need to rationalize the denominator first.
What we are looking for are factors that are multiples of the index, or perfect cubes.
root(3)(25x^11)/root(3)(9w^2)3√25x113√9w2
9 * 3 = 279⋅3=27 meaning 3^333 is 27
w^2 *w = w^3w2⋅w=w3 giving us another perfect cube rationalizing the denominator
root(3)(25x^11)/root(3)(9w^2)*root(3)(3w)/root(3)(3w) = (root(3)125 root(3)(w)root(3)(x^11))/(root(3)(27w^3)3√25x113√9w2⋅3√3w3√3w=3√1253√w3√x113√27w3
In the numerator:
root(3)125 = 5 3√125=5 Is a perfect cube
root(3)w3√w is fully simplified
root(3)x^93√x9 * root(3)x^2 = root(3)x^11⋅3√x2=3√x11
x^(9/3)x93 = x^3x3
root(3)273√27 root(3) w^33√w3 This is the denominator
root(3)27 = 3 3√27=3
root(3)w^3 = w3√w3=w
put it all back together over a single fraction
(5x^3 root(3)(x^2)root(3)w)/(3w)5x33√x23√w3w
