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Answer :
To determine which monomial is a perfect cube, let's analyze each option:
A monomial is considered a perfect cube if it can be expressed as the cube of another integer. We will look for a number that, when raised to the power of 3, matches the coefficient.
1. Option 1: [tex]\( 1x^3 \)[/tex]
- The coefficient here is 1.
- 1 is a perfect cube since [tex]\( 1^3 = 1 \)[/tex].
2. Option 2: [tex]\( 3x^3 \)[/tex]
- The coefficient here is 3.
- 3 is not a perfect cube since there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 3 \)[/tex].
3. Option 3: [tex]\( 6x^3 \)[/tex]
- The coefficient here is 6.
- 6 is not a perfect cube since there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 6 \)[/tex].
4. Option 4: [tex]\( 9x^3 \)[/tex]
- The coefficient here is 9.
- 9 is not a perfect cube since there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 9 \)[/tex].
From this analysis, we can conclude that the monomial [tex]\( 1x^3 \)[/tex] is the only one in the list that qualifies as a perfect cube. Therefore, the answer is [tex]\( 1x^3 \)[/tex].
A monomial is considered a perfect cube if it can be expressed as the cube of another integer. We will look for a number that, when raised to the power of 3, matches the coefficient.
1. Option 1: [tex]\( 1x^3 \)[/tex]
- The coefficient here is 1.
- 1 is a perfect cube since [tex]\( 1^3 = 1 \)[/tex].
2. Option 2: [tex]\( 3x^3 \)[/tex]
- The coefficient here is 3.
- 3 is not a perfect cube since there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 3 \)[/tex].
3. Option 3: [tex]\( 6x^3 \)[/tex]
- The coefficient here is 6.
- 6 is not a perfect cube since there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 6 \)[/tex].
4. Option 4: [tex]\( 9x^3 \)[/tex]
- The coefficient here is 9.
- 9 is not a perfect cube since there is no integer [tex]\( n \)[/tex] such that [tex]\( n^3 = 9 \)[/tex].
From this analysis, we can conclude that the monomial [tex]\( 1x^3 \)[/tex] is the only one in the list that qualifies as a perfect cube. Therefore, the answer is [tex]\( 1x^3 \)[/tex].
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