# Thread: Roots expressed as exponents question

1. ## Roots expressed as exponents question

Hello, the author seems to contradict herself in the following examples. See below

This Is correct
Expression 1:

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

2. It's correct because $(x^3)^{\frac{1}{4}}=x^{3\cdot\frac{1}{4}}=x^{\frac {3}{4}}$

3. Well if thats the case could we take

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

4. Originally Posted by allyourbass2212
Well if thats the case could we take

$= 3xy^{(7\cdot\frac{-1}{5})}$
No.

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

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