Answer :
To determine which monomial is a perfect cube, we need to check the coefficients of each given monomial. A perfect cube is a number that can be expressed as the cube of an integer.
Let's consider the monomials:
1. [tex]\(1x^3\)[/tex]
2. [tex]\(3x^3\)[/tex]
3. [tex]\(6x^3\)[/tex]
4. [tex]\(9x^3\)[/tex]
Here’s how we check each coefficient:
1. Monomial: [tex]\(1x^3\)[/tex]
- Coefficient: 1
- [tex]\(1\)[/tex] is a perfect cube because it can be written as [tex]\(1^3\)[/tex].
2. Monomial: [tex]\(3x^3\)[/tex]
- Coefficient: 3
- 3 is not a perfect cube because there's no integer [tex]\(n\)[/tex] such that [tex]\(n^3 = 3\)[/tex].
3. Monomial: [tex]\(6x^3\)[/tex]
- Coefficient: 6
- 6 is not a perfect cube because there's no integer [tex]\(n\)[/tex] such that [tex]\(n^3 = 6\)[/tex].
4. Monomial: [tex]\(9x^3\)[/tex]
- Coefficient: 9
- 9 is not a perfect cube because there's no integer [tex]\(n\)[/tex] such that [tex]\(n^3 = 9\)[/tex].
Therefore, among the coefficients given, only the coefficient 1 in the monomial [tex]\(1x^3\)[/tex] is a perfect cube. Thus, [tex]\(1x^3\)[/tex] is the monomial that is a perfect cube.
Let's consider the monomials:
1. [tex]\(1x^3\)[/tex]
2. [tex]\(3x^3\)[/tex]
3. [tex]\(6x^3\)[/tex]
4. [tex]\(9x^3\)[/tex]
Here’s how we check each coefficient:
1. Monomial: [tex]\(1x^3\)[/tex]
- Coefficient: 1
- [tex]\(1\)[/tex] is a perfect cube because it can be written as [tex]\(1^3\)[/tex].
2. Monomial: [tex]\(3x^3\)[/tex]
- Coefficient: 3
- 3 is not a perfect cube because there's no integer [tex]\(n\)[/tex] such that [tex]\(n^3 = 3\)[/tex].
3. Monomial: [tex]\(6x^3\)[/tex]
- Coefficient: 6
- 6 is not a perfect cube because there's no integer [tex]\(n\)[/tex] such that [tex]\(n^3 = 6\)[/tex].
4. Monomial: [tex]\(9x^3\)[/tex]
- Coefficient: 9
- 9 is not a perfect cube because there's no integer [tex]\(n\)[/tex] such that [tex]\(n^3 = 9\)[/tex].
Therefore, among the coefficients given, only the coefficient 1 in the monomial [tex]\(1x^3\)[/tex] is a perfect cube. Thus, [tex]\(1x^3\)[/tex] is the monomial that is a perfect cube.
