# How to work a fractional exponent? Need non decimal answer!

• Dec 19th 2010, 07:56 AM
Spoolx
How to work a fractional exponent? Need non decimal answer!
So on a recent test I ran into this, I wasnt sure how to work the first part because I couldnt figure out the fraction for it.

The question said to
PI((4/5(4)^5/4)-(16/3))

My first instinct is to solve the first, then subtract the second from it then multiply it by PI, however I couldnt figure out how to turn the first into a fractional answer.

Any help is appreciated.

Thanks
Rich
• Dec 19th 2010, 08:01 AM
Prove It
Hint:

$\displaystyle a^{\frac{5}{4}} = \sqrt[4]{a^5} = \sqrt[4]{a^4\cdot a} = \sqrt[4]{a^4}\cdot \sqrt[4]{a} = a\sqrt[4]{a}$.
• Dec 19th 2010, 08:04 AM
CaptainBlack
Quote:

Originally Posted by Spoolx
So on a recent test I ran into this, I wasnt sure how to work the first part because I couldnt figure out the fraction for it.

The question said to
PI((4/5(4)^5/4)-(16/3))

My first instinct is to solve the first, then subtract the second from it then multiply it by PI, however I couldnt figure out how to turn the first into a fractional answer.

Any help is appreciated.

Thanks
Rich

$4^{5/4}=(4^{1/4})^5=(\sqrt{2})^5=4\sqrt{2}$

If we are interested in the positive and negative values there would be a $\pm$ in front

CB