Let's determine the degrees of the given monomials step-by-step.
1. Monomial: 4
- The monomial [tex]\(4\)[/tex] is a constant term.
- Constants are considered to have a degree of 0 because they do not have any variables.
- Therefore, the degree of the monomial [tex]\(4\)[/tex] is:
[tex]\[ \boxed{0} \][/tex]
2. Monomial: [tex]\(2z\)[/tex]
- The monomial [tex]\(2z\)[/tex] has a variable [tex]\(z\)[/tex] with an exponent of 1.
- To find the degree, sum the exponents of all the variables in the monomial.
- Here, the only variable is [tex]\(z\)[/tex] with an exponent of 1.
- Therefore, the degree of the monomial [tex]\(2z\)[/tex] is:
[tex]\[ \boxed{1} \][/tex]
3. Monomial: [tex]\(4r^2st^3\)[/tex]
- The monomial [tex]\(4r^2st^3\)[/tex] has variables [tex]\(r\)[/tex], [tex]\(s\)[/tex], and [tex]\(t\)[/tex] with exponents.
- [tex]\(r\)[/tex] has an exponent of 2.
- [tex]\(s\)[/tex] has an implicit exponent of 1.
- [tex]\(t\)[/tex] has an exponent of 3.
- To find the degree, sum the exponents of all the variables in the monomial.
- Therefore, the sum is [tex]\(2 + 1 + 3 = 6\)[/tex].
- The degree of the monomial [tex]\(4r^2st^3\)[/tex] is:
[tex]\[ \boxed{6} \][/tex]
4. Monomial: [tex]\(3xyz^2\)[/tex]
- The monomial [tex]\(3xyz^2\)[/tex] has variables [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] with exponents.
- [tex]\(x\)[/tex] has an implicit exponent of 1.
- [tex]\(y\)[/tex] has an implicit exponent of 1.
- [tex]\(z\)[/tex] has an exponent of 2.
- To find the degree, sum the exponents of all the variables in the monomial.
- Therefore, the sum is [tex]\(1 + 1 + 2 = 4\)[/tex].
- The degree of the monomial [tex]\(3xyz^2\)[/tex] is:
[tex]\[ \boxed{4} \][/tex]
Therefore, the degrees of the given monomials are:
- For [tex]\(4\)[/tex]: [tex]\(\boxed{0}\)[/tex]
- For [tex]\(2z\)[/tex]: [tex]\(\boxed{1}\)[/tex]
- For [tex]\(4r^2st^3\)[/tex]: [tex]\(\boxed{6}\)[/tex]
- For [tex]\(3xyz^2\)[/tex]: [tex]\(\boxed{4}\)[/tex]
