To find the degree of each monomial, we need to determine the sum of the exponents of the variables present in each monomial. Let's analyze each monomial step by step.
1. For the monomial [tex]\(4\)[/tex]:
- There are no variables in this monomial.
- The degree of a constant term is [tex]\(0\)[/tex].
Therefore, the degree of [tex]\(4\)[/tex] is [tex]\(0\)[/tex].
2. For the monomial [tex]\(2z\)[/tex]:
- There is one variable, [tex]\(z\)[/tex], with an implicit exponent of [tex]\(1\)[/tex].
Therefore, the degree of [tex]\(2z\)[/tex] is [tex]\(1\)[/tex].
3. For the monomial [tex]\(4r^2 s t^3\)[/tex]:
- The variable [tex]\(r\)[/tex] has an exponent of [tex]\(2\)[/tex].
- The variable [tex]\(s\)[/tex] has an implicit exponent of [tex]\(1\)[/tex].
- The variable [tex]\(t\)[/tex] has an exponent of [tex]\(3\)[/tex].
- The degree of the monomial is the sum of these exponents: [tex]\(2 + 1 + 3 = 6\)[/tex].
Therefore, the degree of [tex]\(4r^2 s t^3\)[/tex] is [tex]\(6\)[/tex].
4. For the monomial [tex]\(3xyz^2\)[/tex]:
- The variable [tex]\(x\)[/tex] has an implicit exponent of [tex]\(1\)[/tex].
- The variable [tex]\(y\)[/tex] has an implicit exponent of [tex]\(1\)[/tex].
- The variable [tex]\(z\)[/tex] has an exponent of [tex]\(2\)[/tex].
- The degree of the monomial is the sum of these exponents: [tex]\(1 + 1 + 2 = 4\)[/tex].
Therefore, the degree of [tex]\(3xyz^2\)[/tex] is [tex]\(4\)[/tex].
To summarize, the degrees of the given monomials are:
- Degree of [tex]\(4\)[/tex]: [tex]\(0\)[/tex]
- Degree of [tex]\(2z\)[/tex]: [tex]\(1\)[/tex]
- Degree of [tex]\(4r^2 s t^3\)[/tex]: [tex]\(6\)[/tex]
- Degree of [tex]\(3xyz^2\)[/tex]: [tex]\(4\)[/tex]
