To find the degree of the monomial [tex]\(2s^3 t^a\)[/tex], we need to consider the exponents of the variables [tex]\(s\)[/tex] and [tex]\(t\)[/tex] involved in the term. The degree of a monomial is the sum of the exponents of the variables.
In the monomial [tex]\(2s^3 t^a\)[/tex]:
- The coefficient [tex]\(2\)[/tex] does not affect the degree since it is a constant.
- The exponent of [tex]\(s\)[/tex] is [tex]\(3\)[/tex].
- The exponent of [tex]\(t\)[/tex] is [tex]\(a\)[/tex].
Therefore, the degree of [tex]\(2s^3 t^a\)[/tex] is the sum of the exponents of [tex]\(s\)[/tex] and [tex]\(t\)[/tex], which is [tex]\(3 + a\)[/tex].
Given the possible degrees [tex]\(4\)[/tex], [tex]\(5.5\)[/tex], and [tex]\(7\)[/tex], we need to determine if these values could be achieved by suitable choices of [tex]\(a\)[/tex]:
1. Degree 4:
- Set the degree equal to [tex]\(4\)[/tex]: [tex]\(3 + a = 4\)[/tex].
- Solving for [tex]\(a\)[/tex]: [tex]\(a = 4 - 3 = 1\)[/tex].
- So, if [tex]\(a = 1\)[/tex], the degree of [tex]\(2s^3 t^1\)[/tex] is [tex]\(4\)[/tex].
2. Degree 5.5:
- Set the degree equal to [tex]\(5.5\)[/tex]: [tex]\(3 + a = 5.5\)[/tex].
- Solving for [tex]\(a\)[/tex]: [tex]\(a = 5.5 - 3 = 2.5\)[/tex].
- So, if [tex]\(a = 2.5\)[/tex], the degree of [tex]\(2s^3 t^{2.5}\)[/tex] is [tex]\(5.5\)[/tex].
3. Degree 7:
- Set the degree equal to [tex]\(7\)[/tex]: [tex]\(3 + a = 7\)[/tex].
- Solving for [tex]\(a\)[/tex]: [tex]\(a = 7 - 3 = 4\)[/tex].
- So, if [tex]\(a = 4\)[/tex], the degree of [tex]\(2s^3 t^4\)[/tex] is [tex]\(7\)[/tex].
Hence, the possible degrees that the monomial [tex]\(2s^3 t^a\)[/tex] can assume from the given values are:
- [tex]\(4\)[/tex]
- [tex]\(5.5\)[/tex]
- [tex]\(7\)[/tex]
