Question

How do you simplify `(5q^-2t^6)/(10q^2t^-4)`?

Answer 1

`color(blue)(t^10/(2q^4)`

Explanation:

`(cancel5^color(blue)1q^-2t^6)/(cancel10^color(blue)2q^2t^-4)`

`:.=t^(6+4)/(2q^(2+2))`

`color(red)({t^6/t^-4=(t^6/1)/(1/t^4)=t^6/1 xx t^4/1=t^(6+4)=t^10}`

`color(red)({q^-2/q^2=(1/q^2)/((q^2)/1)=1/q^2 xx 1/q^2=1/q^(2+2)=1/q^4}`

`:.=color(blue)(t^10/(2q^4)`