1. ## Properites of Derivatives question about the power rule

Hi I have this question:

$\displaystyle \sqrt{4x^3}$

so I cann use the power rule to rewrite this question correct? so it would be like so:

$\displaystyle 2\sqrt{x^3}$

It is the next step I'm confused about.

$\displaystyle 2(x^3)^\frac{1}{ 2}$

how do you get the 1/2 exponent?

2. Originally Posted by sara213
Hi I have this question:

$\displaystyle \sqrt{4x^3}$

so I cann use the power rule to rewrite this question correct? so it would be like so:

$\displaystyle 2\sqrt{x^3}$

It is the next step I'm confused about.

$\displaystyle 2(x^3)^\frac{1}{ 2}$

how do you get the 1/2 exponent?

Hello Sara.

$\displaystyle \sqrt[n]{x^m}=x^{\frac{m}{n}}$

and:

$\displaystyle (x^a)^b=x^{ab}$

3. This is simply the definition of square root. An nth root is simply the exponent 1/n.

4. you know i kind of feel stupid to ask that question...because I knew that....sorry guys...><

but I think i just needed confirmation is all. thanks