What is the degree of this monomial 17x^5y^2

The degree of this monomial, which is a form of a polynomial, has a degree of 7.

Explanation: For two variables, we take the sum of the powers and this becomes the highest power of our polynomial, which is defined as the degree of a polynomial.
Now, it's relatively easy for polynomials where we are taking one variable, but two variables is a little bit harder.

Notice how any variable to the power of 0 will give us 1, and anything multiplied by 0 will give us 0.

We can rewrite this in many different ways:


Since every other factor cancels out to be 0, then we say that they are non-existent, because even, if in hindsight they do exist, they don't affect our final polynomial.

So, we can say that the degree of this polynomial, highest power, is 7.