Answer :

To find the degree of a polynomial, we look for the term with the highest sum of the exponents of its variables. Let's break down each term of the polynomial and find their degrees:

1. Term 1: [tex]\(x^3 y^3\)[/tex]
- The exponents of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are 3 each.
- Sum of the exponents = [tex]\(3 + 3 = 6\)[/tex].

2. Term 2: [tex]\(-4\)[/tex]
- This is a constant term with no variables.
- Degree of a constant is 0.

3. Term 3: [tex]\(9 y^3 w^7 x^7\)[/tex]
- The exponents are 3 for [tex]\(y\)[/tex], 7 for [tex]\(w\)[/tex], and 7 for [tex]\(x\)[/tex].
- Sum of the exponents = [tex]\(3 + 7 + 7 = 17\)[/tex].

4. Term 4: [tex]\(4 w\)[/tex]
- The exponent of [tex]\(w\)[/tex] is 1.
- Sum of the exponents = [tex]\(1\)[/tex].

Now, compare the degrees of all the terms:
- Term 1: Degree 6
- Term 2: Degree 0
- Term 3: Degree 17
- Term 4: Degree 1

The degree of the entire polynomial is determined by the term with the highest degree. Therefore, the degree of the polynomial is 17.

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