I really need a hint on the following question:
''Let there be $(x_0,y_0,z_0)$ a point of the surface ${x^a + y^a +z^a = 1},z>0,y>0,x>0$. $P$ is the plane which is tangent at the point. Calculate the volume of the pyramid bounded by $P,z=0,y=0,x=0$.''
Attempt at a Solution:
I know that I should probably take the partial derivatives of ${x^a + y^a +z^a = 1}$ and use them as a normal vector in the equation: 
however what makes it difficult for me to solve this is that I can't imagine this in 3d, nor can I understand how can I calculate volume if $(x_0,y_0,z_0)$ is only given parametrically.
Hint: First, you need to get the tangent plane equation $$ A(x-x_0)+B(y-y_0)+C(z-z_0)=0 $$ where $(A,B,C)$ is a normal vector to the plane. After that, find the intersections of the plane with the three axes by setting suitable values of $x,y,z$ in the plane equation. Once you know the lengths of the sides, you can calculate the volume.