# How do find the quotient of (-4sqrt3 )/( 3sqrt2)?

Nov 8, 2015

• Rewrite the square roots to exponents
• A little bit of algebra
.. and you will get the answer $- \frac{\sqrt{8}}{\sqrt{3}}$

#### Explanation:

Sometimes square roots can be painful to work with, so we have some rules that we can use to rewrite them. One of them is:
$\sqrt{a} = {a}^{\frac{1}{2}}$
And this is the one we will use for this problem.

We also need to know how to deal with eventual negative exponents. Let's have an example:
${a}^{- n} = \frac{1}{{a}^{n}}$
In this problem, we will use this rule the other way around as well. So let's start!

To make it easier for us, we can split up the expression into parts; one for the base of 2, and one of the base of 3:

$\frac{- 4 \sqrt{3}}{3 \sqrt{2}} = \frac{- 4}{\sqrt{2}} \cdot \frac{\sqrt{3}}{3}$

Let's tweek on the expression so we can see the exponents

$- {2}^{2} / {2}^{\frac{1}{2}} \cdot {3}^{\frac{1}{2}} / 3$

Now, let's move the factors to the same place, using the formula ${a}^{- n} = \frac{1}{{a}^{n}}$:

$\frac{- {2}^{2} \cdot {2}^{- \frac{1}{2}}}{1} \cdot \frac{1}{{3}^{1} \cdot {3}^{- \frac{1}{2}}}$
= -2^(2/2-1/2)/1 * 1/(3^(2/2 - 1/2)
$= - {2}^{\frac{3}{2}} / 1 \cdot \frac{1}{3} ^ \left(\frac{1}{2}\right)$
$= - \frac{\sqrt{{2}^{3}}}{\sqrt{3}}$
$= - \frac{\sqrt{8}}{\sqrt{3}}$