Answer :
To determine which monomial is a perfect cube, we need to look at the coefficients of the monomials provided. A number is a perfect cube if it can be expressed as [tex]\( n^3 \)[/tex] where [tex]\( n \)[/tex] is an integer.
Let's examine each coefficient:
1. Coefficient 1:
- [tex]\(1\)[/tex] can be written as [tex]\(1^3\)[/tex] because [tex]\(1 \times 1 \times 1 = 1\)[/tex].
2. Coefficient 3:
- The cube root of [tex]\(3\)[/tex] is not an integer, so [tex]\(3\)[/tex] is not a perfect cube.
3. Coefficient 6:
- The cube root of [tex]\(6\)[/tex] is not an integer, so [tex]\(6\)[/tex] is not a perfect cube.
4. Coefficient 9:
- The cube root of [tex]\(9\)[/tex] is not an integer, so [tex]\(9\)[/tex] is not a perfect cube.
From the list above, only the monomial with coefficient [tex]\(1\)[/tex], or [tex]\(1x^3\)[/tex], is a perfect cube because [tex]\(1\)[/tex] is a perfect cube.
Therefore, the monomial that is a perfect cube is [tex]\(1x^3\)[/tex].
Let's examine each coefficient:
1. Coefficient 1:
- [tex]\(1\)[/tex] can be written as [tex]\(1^3\)[/tex] because [tex]\(1 \times 1 \times 1 = 1\)[/tex].
2. Coefficient 3:
- The cube root of [tex]\(3\)[/tex] is not an integer, so [tex]\(3\)[/tex] is not a perfect cube.
3. Coefficient 6:
- The cube root of [tex]\(6\)[/tex] is not an integer, so [tex]\(6\)[/tex] is not a perfect cube.
4. Coefficient 9:
- The cube root of [tex]\(9\)[/tex] is not an integer, so [tex]\(9\)[/tex] is not a perfect cube.
From the list above, only the monomial with coefficient [tex]\(1\)[/tex], or [tex]\(1x^3\)[/tex], is a perfect cube because [tex]\(1\)[/tex] is a perfect cube.
Therefore, the monomial that is a perfect cube is [tex]\(1x^3\)[/tex].
