Let's determine the degree of each given monomial step by step.
1. Monomial: [tex]\(4\)[/tex]
- The term [tex]\(4\)[/tex] is a constant, and a constant has a degree of [tex]\(0\)[/tex].
- Degree: 0
2. Monomial: [tex]\(2z\)[/tex]
- The term [tex]\(2z\)[/tex] involves a single variable [tex]\(z\)[/tex] raised to the power of [tex]\(1\)[/tex].
- Degree: 1
3. Monomial: [tex]\(4r^2st^3\)[/tex]
- This monomial involves three variables: [tex]\(r\)[/tex], [tex]\(s\)[/tex], and [tex]\(t\)[/tex].
- The variable [tex]\(r\)[/tex] is raised to the power of [tex]\(2\)[/tex].
- The variable [tex]\(s\)[/tex] is implicitly raised to the power of [tex]\(1\)[/tex] (since [tex]\(s\)[/tex] without an exponent is taken as [tex]\(s^1\)[/tex]).
- The variable [tex]\(t\)[/tex] is raised to the power of [tex]\(3\)[/tex].
- To find the degree of the monomial, sum the exponents of all the variables: [tex]\(2 + 1 + 3 = 6\)[/tex].
- Degree: 6
4. Monomial: [tex]\(3xyz^2\)[/tex]
- This monomial involves three variables: [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex].
- The variable [tex]\(x\)[/tex] is raised to the power of [tex]\(1\)[/tex] (since [tex]\(x\)[/tex] without an exponent is taken as [tex]\(x^1\)[/tex]).
- The variable [tex]\(y\)[/tex] is raised to the power of [tex]\(1\)[/tex].
- The variable [tex]\(z\)[/tex] is raised to the power of [tex]\(2\)[/tex].
- To find the degree of the monomial, sum the exponents of all the variables: [tex]\(1 + 1 + 2 = 4\)[/tex].
- Degree: 4
So, the degrees of the given monomials are:
- [tex]\(4\)[/tex]: Degree: 0
- [tex]\(2z\)[/tex]: Degree: 1
- [tex]\(4r^2st^3\)[/tex]: Degree: 6
- [tex]\(3xyz^2\)[/tex]: Degree: 4
