$a)w\left(x\right)=x^2-1+x^3-x^4-x^5=-x^5-x^4+x^3+x^2-1,st\left(w\right)=5$

$b)w\left(x\right)=2x-3x^5+7x^6-3x^2-2=7x^6-3x^5-3x^2+2x-2,st\left(w\right)=6$

$c)w\left(x\right)=\frac{1}{2}{x}^6-x^2+\frac{3}{4}{x}^8-\frac{1}{4}{x}^5+7=\frac{3}{4}{x}^8+\frac{1}{2}{x}^6-\frac{1}{4}{x}^5-x^2+7,st\left(w\right)=8$

$d)w\left(x\right)=\sqrt{2}{x}^3-x+\left(1-\sqrt{2}\right)x^9=\left(1-\sqrt{2}\right)x^9+\sqrt{2}{x}^3-x,st\left(w\right)=9$