The marginal product of labor

The production function is:
where a > 0 and b > 0.

1. The marginal product of labor is:
2. The marginal product of labor is:
3. The marginal rate of technical substitution is:
4. Show that the isoquants for this production function are convex. (Show that MRTS diminishes as L increases. Why?)
5. Derive the equation for the long-run expansion path