Simplifying Expression with Laws of Exponents

[reenmachine]

Homework Statement

Simplify the following expression:

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

Homework 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!

 

[Dick]

Homework Statement

Simplify the following expression:

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

Homework 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!

Looks fine to me.

 

[reenmachine]

Looks fine to me.

thank you!

 

[Mark44]

Minor point: the word is exponent.

 

[reenmachine]

Minor point: the word is exponent.

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

Thank you!