- #1
reenmachine
Gold Member
- 514
- 8
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!
Last edited: