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Answer :
To determine which number in the monomial [tex]\(215 x^{18} y^3 z^{21}\)[/tex] needs to be changed to make it a perfect cube, we need all the components (the coefficient and the exponents) to be multiples of 3.
Here's how we can check each part:
1. Look at the Coefficient: 215
Check if 215 is a multiple of 3 by dividing it by 3.
[tex]\(215 \div 3 \)[/tex] gives a remainder of 2, which means 215 is not a multiple of 3.
2. Check the Exponents:
- For [tex]\(x^{18}\)[/tex]:
The exponent 18 is already a multiple of 3 because [tex]\(18 \div 3 = 6\)[/tex] with no remainder.
- For [tex]\(y^3\)[/tex]:
The exponent 3 is also a multiple of 3 because [tex]\(3 \div 3 = 1\)[/tex] with no remainder.
- For [tex]\(z^{21}\)[/tex]:
The exponent 21 is a multiple of 3 because [tex]\(21 \div 3 = 7\)[/tex] with no remainder.
From this analysis, the issue is with the coefficient 215, which is not a multiple of 3. Therefore, the number in the monomial that needs to be changed to make it a perfect cube is 215.
Here's how we can check each part:
1. Look at the Coefficient: 215
Check if 215 is a multiple of 3 by dividing it by 3.
[tex]\(215 \div 3 \)[/tex] gives a remainder of 2, which means 215 is not a multiple of 3.
2. Check the Exponents:
- For [tex]\(x^{18}\)[/tex]:
The exponent 18 is already a multiple of 3 because [tex]\(18 \div 3 = 6\)[/tex] with no remainder.
- For [tex]\(y^3\)[/tex]:
The exponent 3 is also a multiple of 3 because [tex]\(3 \div 3 = 1\)[/tex] with no remainder.
- For [tex]\(z^{21}\)[/tex]:
The exponent 21 is a multiple of 3 because [tex]\(21 \div 3 = 7\)[/tex] with no remainder.
From this analysis, the issue is with the coefficient 215, which is not a multiple of 3. Therefore, the number in the monomial that needs to be changed to make it a perfect cube is 215.
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