$$8^{}- 5^{17} \times 2^{20}$$ is divided by - 9 then what is the remainder?

We can find the remainder on dividing by 9 and then find the negative remainder in order to find the reminder we would have gotten on dividing by -9. 
$$\left[\frac{8-5^{17}\times\ 2^{20}}{9}\right]_R$$
$$\left[\frac{8}{9}\right]_R-\left[\frac{5^{17}\times\ 2^{17}\times\ 2^3}{9}\right]_R$$
$$-1-\left[\frac{10^{17}}{9}\right]_R\times\ \left[\frac{8}{9}\right]_R$$
$$-1-1^{17}\times\ \left(-1\right)$$
$$-1+1\ =\ 0$$
Upon reversing the sign to calculate the remainder on dividing it by -9, we get 0 again. 
Hence, the remainder is 0.