Question

How do you simplify `((4t^3)(2t))/(20t^2)` and what are the excluded values for the variable?

Answer 1

`((4t^3)(2t))/(20t^2)=color(green)(2/5t^2)`
`color(white)("XXXXXXXXXXXXXXXX")color(red)(t!=0)`

Explanation:

`color(red)(t=0)` must be excluded since this would result in an undefined expression value: `0/0`

`((4t^3)(2t))/(20t^2)`
`color(white)("XXX")=((color(blue)(cancel(color(black)4))color(magenta)(cancel(color(black)(t^3))^t))(2t))/(color(blue)(cancel(color(black)(20))_5)color(magenta)(cancel(color(black)(t^2))))`

`color(white)("XXX")=(2t^2)/5`