c# - Static vs. non-static method

Question

Suppose you have some method that could be made static, inside a non-static class.
For example:

private double power(double a, double b)
    {
        return (Math.Pow(a, b));
    }

Do you see any benefit from changing the method signature into static? In the example above:

private static double power(double a, double b)
    {
        return (Math.Pow(a, b));
    }

Even if there is some performance or memory gain, wouldn't the compiler do it as a simple optimization in compile time?

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Edit: What I am looking for are the benefits by declaring the method as static. I know that this is the common practice. I would like to understand the logic behind it.
And of course, this method is just an example to clarify my intention.

Answer 1

As defined, power is stateless and has no side effects on any enclosing class so it should be declared static.

This article from MSDN goes into some of the performance differences of non-static versus static. The call is about four times faster than instantiating and calling, but it really only matters in a tight loop that is a performance bottleneck.