Answer :
To determine which monomial is a perfect cube, we need to analyze the coefficients of the monomials because the variable part, [tex]\( x^3 \)[/tex], is already a perfect cube.
A monomial is a perfect cube if both its coefficient and its variable part are perfect cubes. Let's look at the coefficients of the given monomials:
1. [tex]\( 1x^3 \)[/tex]
2. [tex]\( 3x^3 \)[/tex]
3. [tex]\( 6x^3 \)[/tex]
4. [tex]\( 9x^3 \)[/tex]
We need to check if the coefficients 1, 3, 6, and 9 are perfect cubes. A perfect cube is a number that can be expressed as the cube of an integer.
- The coefficient 1 is a perfect cube because [tex]\( 1^3 = 1 \)[/tex].
- The coefficient 3 is not a perfect cube because there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 3 \)[/tex].
- The coefficient 6 is not a perfect cube because there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 6 \)[/tex].
- The coefficient 9 is not a perfect cube because there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 9 \)[/tex].
Therefore, out of the given monomials, [tex]\( 1x^3 \)[/tex] is the perfect cube, as its coefficient 1 is a perfect cube.
A monomial is a perfect cube if both its coefficient and its variable part are perfect cubes. Let's look at the coefficients of the given monomials:
1. [tex]\( 1x^3 \)[/tex]
2. [tex]\( 3x^3 \)[/tex]
3. [tex]\( 6x^3 \)[/tex]
4. [tex]\( 9x^3 \)[/tex]
We need to check if the coefficients 1, 3, 6, and 9 are perfect cubes. A perfect cube is a number that can be expressed as the cube of an integer.
- The coefficient 1 is a perfect cube because [tex]\( 1^3 = 1 \)[/tex].
- The coefficient 3 is not a perfect cube because there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 3 \)[/tex].
- The coefficient 6 is not a perfect cube because there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 6 \)[/tex].
- The coefficient 9 is not a perfect cube because there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 9 \)[/tex].
Therefore, out of the given monomials, [tex]\( 1x^3 \)[/tex] is the perfect cube, as its coefficient 1 is a perfect cube.
