When are we suppose to Rationalize the denominator?
Like here, 1/[tex] \sqrt[4]{x^3} [/tex] Is that the final answer? How come we can't rationalize this denominator?
And other example---- x^-1/5 and my teacher said the answer for this one is - 1/[tex] \sqrt[5]{x} [/tex] How come? Can't we rationalize the denominator?
This is so hard? Can somebody help please?
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
