Answer :

To determine which monomial is a perfect cube among the given options, we need to check if the coefficient of each monomial is a perfect cube. A perfect cube is a number that can be expressed as the cube of an integer.

Let's examine each monomial:

1. Monomial: [tex]\(1x^3\)[/tex]
The coefficient is 1.
Since [tex]\(1 = 1^3\)[/tex], 1 is a perfect cube.

2. Monomial: [tex]\(3x^3\)[/tex]
The coefficient is 3.
There's no integer that if cubed gives 3, so 3 is not a perfect cube.

3. Monomial: [tex]\(6x^3\)[/tex]
The coefficient is 6.
Similarly, no integer cubed will result in 6. Therefore, 6 is not a perfect cube.

4. Monomial: [tex]\(9x^3\)[/tex]
The coefficient is 9.
Since [tex]\(9 = 3^2\)[/tex] and not [tex]\(a^3\)[/tex] for any integer [tex]\(a\)[/tex], 9 is not a perfect cube.

From these evaluations, we find that the only coefficient that is a perfect cube is 1. Therefore, the monomial [tex]\(1x^3\)[/tex] is a perfect cube.

Thanks for taking the time to read Which monomial is a perfect cube A tex 1x 3 tex B tex 3x 3 tex C tex 6x 3 tex D tex 9x 3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada