[tex] \frac{x*x^2*x^3*.....*x^{100}}{x^2*x^4*x^6*....*x^{100}}= \frac{x^{1+2+3+.....+100}}{x^{2+4+6+.....+100}} \\ \\
1+2+3+....+100= \frac{100(100+1)}{2}=50*101=5050 \\
2+4+6+....+100=2(1+2+3+....+50)=2* \frac{50(50+1)}{2} =50*51 \\=2550 \\ \\
\frac{x^{5050}}{x^{2550}}^{(25}=\boxed{x^{2500}}[/tex]
