how can you tell if an answer will be positive or negative for negative eponents

you cant. Lets take for example an equation of the form a₀+a₁*x^t₁+a₂*x^t₂+a₃*x^t₃..........a_n*x^t_n=0,

 

where t₁ 2 3<..... n<0

 

Now multiply by x^-t₁ and get: a₀*x^-t₁+a₁+a₂*x^t₂-t₁+a₃*x^t₃-t₁+a₄*x^t₄-t₁+a₅*x^t₅-t₁..........a_n*x^t_n-t₁=0

 

the equation is exactly the same, no solution was added (you can check it)

 

So it doesnt tell anything about the answer.