Question 82505
Lets say you had 


{{{sqrt(x)*root(3,x)}}}


how would you simplify this? Well since we have a square root and a cube root, we cannot mix the two expressions. In order to simplify, you would have to raise everything to the 6th power like this:


{{{(sqrt(x)*root(3,x))^6}}}


and simplify


{{{x^3*x^2}}}


{{{x^5}}}


{{{root(6,x^5)=x^(5/6)}}}


But simplification gets tricky. However, since this expression is true


*[Tex \LARGE \sqrt[n]{x^m}=x^{\frac{m}{n}}]


We'll have an easier way to simplify. So we can let {{{sqrt(x)}}} become *[Tex \LARGE x^{\frac{1}{2}}] and {{{root(3,x)}}} become *[Tex \LARGE x^{\frac{1}{3}}]. So we'll get:


*[Tex \LARGE x^{\frac{1}{2}}*x^{\frac{1}{3}}=x^{\frac{1}{2}+\frac{1}{3}}=x^{\frac{5}{6}}].  


This is just one of the many examples where exponent notation is easier to use.