Find the max/min values of a function when (x,y) is a point in the set...

This normally wouldn't be so hard for me, except for the awkward constraint we've been given.

Find the maximum and minimum values of the function

$\displaystyle f(x,y)=2x^4-4x^2y^2+5y^4$

when $\displaystyle (x,y)$ is a point in the set

$\displaystyle \{(x,y):x^4+y^4\leq 80\}$.

I've been told that using Lagrange Multipliers is the proper method to solve this, but I'm not so sure. I'm new to using Lagrange Multipliers, and I haven't seen a question for which the constraint is a set that doesn't have a definite value.