# Roots expressed as exponents question

• August 2nd 2009, 10:08 PM
allyourbass2212
Roots expressed as exponents question
Hello, the author seems to contradict herself in the following examples. See below

This Is correct
Expression 1:
http://www.mathhelpforum.com/math-he...fc088a16-1.gif

Expression 2:
I think the author did this incorrectly
$\sqrt[4]{x^3}=x^{3/4}$

If we follow the logic of expression 1 should it should be $\sqrt[4]{x^3}=(x^3)^{1/4}$

Thanks
• August 2nd 2009, 10:12 PM
red_dog
It's correct because $(x^3)^{\frac{1}{4}}=x^{3\cdot\frac{1}{4}}=x^{\frac {3}{4}}$
• August 2nd 2009, 10:28 PM
allyourbass2212
Well if thats the case could we take
http://www.mathhelpforum.com/math-he...fc088a16-1.gif

$= 3xy^{(7\cdot\frac{-1}{5})}$
• August 2nd 2009, 11:08 PM
red_dog
Quote:

Originally Posted by allyourbass2212
Well if thats the case could we take
http://www.mathhelpforum.com/math-he...fc088a16-1.gif

$= 3xy^{(7\cdot\frac{-1}{5})}$

No.

$(3xy^7)^{-\frac{1}{5}}=3^{-\frac{1}{5}}x^{-\frac{1}{5}}y^{-\frac{7}{5}}$

Remember that $(ab)^n=a^nb^n$