it is encouraged to rationalize the denomenator
you can rationalize the denomenator
one way is to convert to exponent
and remember your exponential rules
remember that [tex] \sqrt[n]{x^m}=x^{\frac{m}{n}} [/tex]
also, [tex](x^a)(x^b)=x^{a+b}[/tex]
and [tex]x^{-m}=\frac{1}{x^m}[/tex]
so
[tex]\frac{1}{\sqrt[4]{x^3}}=\frac{1}{x^{\frac{3}{4}}}[/tex]
so we want x^{4/4}, so 1/4+3/4=4/4
times the whole thing by [tex]\frac{x^{\frac{1}{4}}}{x^{\frac{1}{4}}}[/tex] to get
[tex]\frac{x^{\frac{1}{4}}}{x^{\frac{4}{4}}}=\frac{x^{\frac{1}{4}}}{x}=\frac{\sqrt[4]{x}}{x}[/tex]
but, it looks alot nicer in the original form tho
the 2nd one, we multiply it by [tex]\frac{x^{\frac{4}{5}}}{x^{\frac{4}{5}}}[/tex] to get [tex]\frac{x^{\frac{4}{5}}}{x}=\frac{\sqrt[5]{x^4}}{x}[/tex]
but it looks nicer in original form tho
so you can ratinalize the denomenator but you don't always have to
