# Homework Help: Laws of exponants

1. Jun 13, 2013

### reenmachine

1. The problem statement, all variables and given/known data

Simplify the following expression:

$\frac{(100^3)^\frac{2}{3}}{1000^\frac{1}{3}}$ ÷ $\left( \frac{-10^2}{100^\frac{1}{2}} \right)^3$

2. Relevant equations

Start with this side: $\frac{(100^3)^\frac{2}{3}}{1000^\frac{1}{3}}$

$\frac{((10^2)^3)^\frac{2}{3}}{(10^3)^\frac{1}{3}}$

$\frac{(10^6)^\frac{2}{3}}{10}$

$\frac{10^4}{10}$

$10^3$

We keep this and go on the right side of the expression:

$\left( \frac{-10^2}{100^\frac{1}{2}} \right)^3$

$\left( \frac{-10^2}{(10^2)\frac{1}{2}} \right)^3$

$\left( \frac{-10^2}{10} \right)^3$

$\left( \frac{-10^6}{10^3} \right)$

$-10^3$

Then we take the two results:

$\frac{10^3}{-10^3}$

$-1$

Is that a correct way to use the laws of exponants?

thank you!

Last edited: Jun 13, 2013
2. Jun 13, 2013

### Dick

Looks fine to me.

3. Jun 13, 2013

### reenmachine

thank you!

4. Jun 14, 2013

### Staff: Mentor

Minor point: the word is exponent.

5. Jun 14, 2013

### reenmachine

Oops , in french it's "exposant" , that's probably where the confusion came from.

Thank you!