# Rationalize a fraction with fractional exponent

• January 22nd 2013, 08:30 PM
petenice
Rationalize a fraction with fractional exponent
My question is, how are they getting from step 2 to step 3. Where is the 3^4/5 coming from?!

Not sure i understand the rationalize the denominator of (1/3)^1/5

Thanks for the help.
• January 22nd 2013, 10:27 PM
hollywood
Re: Rationalize a fraction with fractional exponent
You have $\left( \frac{1}{3} \right)^\frac{1}{5} = \frac{1^\frac{1}{5}}{3^\frac{1}{5}} = \frac{1}{3^\frac{1}{5}}$ and you want to get the fractional exponent out of the denominator. You can multiply top and bottom by whatever you like (except 0). Of course, you choose $3^{\frac{4}{5}}$ so that the denominator will be just 3. That's where $3^{\frac{4}{5}}$ comes from.

And so you get $\frac{1}{3^\frac{1}{5}} = \frac{3^{\frac{4}{5}}}{3^\frac{1}{5}3^{\frac{4}{5} }} = \frac{3^\frac{4}{5}}{3} = \frac{1}{3} \, 3^\frac{4}{5}$.

- Hollywood