How to solve the system $x y^5=8000$ and $x y^4>4100$? I need help getting this equation solved for a website I am building. I am pretty bad at math and am only in pre-algebra. I don't know how I would go about canceling out the ^5 and ^4 because I can't square-root it. Thank you for your help.
$$x y^5=8000$$
and 
$$x y^4>4100$$

From the first equation $x = \frac{8000}{y^5}$, plugging into the inequality, you have:
$$\left(\frac{8000}{y^5} \right)y^4 > 4100$$
$$\frac{8000}{y} > 4100$$
If $y < 0$, the inequality does not hold. If $y>0$, you have $y < \frac{8000}{4100} = \frac{80}{41}$. So the equation and inequality are both satisfied only for points:
$$(x,y) = \left( \frac{8000}{y^5}, y\right), \text{ where } 0 < y < \frac{80}{41}$$
