Reducing a fraction: (-20t^5u^2v^3)/(48t^7u^4v)

[grpriest]

Here's a tough one. I know that there is a method of madness here and once I'm shown the first time, I will understand.

Problem:

Reduce the fraction -20t^5u^2v^3 / 48t^7u^4v

Please get me started and I will be able to get this right!

Thanks so much.

 

[stapel]

If you're not sure about the exponent rules you memorized, then factor everything out:

. . . . .\(\displaystyle \L \frac{-20 t^5 u^2 v^3}{48 t^7 u^4 v}\,= \,\frac{-1\times2\times 2\times 5 \times\,t\,t\,t\,t\,t\,u\,u\,v\,v\,v}{2\times 2\times 2\times 2\times 2\times 3 \times\,t\,t\,t\,t\,t\,t\,t\,u\,u\,u\,u\,v}\)

Then cancel the duplicate factors, and simplify whatever remains.

Eliz.