Final answer:
Option D). The greatest common monomial factor of 18⁴Y + 9 XY⁷ is 9XY. The provided options do not include this factor, making the correct answer (d) None of the above.
Step-by-step explanation:
The challenge is to determine the two terms' highest common monomial factor, 18⁴Y + 9 XY⁷. The greatest monomial that divides both words without a remainder must be found in order to accomplish this. Let's start by examining the coefficients. 9 is the highest common factor between 18´ and 9. Y is a variable that both words share, but its powers differ. The phrase that will have the largest common factor is the one with the lower power of Y. The lowest power of Y in this instance is Y¹ (from the first term).
Let's now examine the variable X. X can be included in the greatest common factor to the smallest power it appears in among the terms, which is X¹, because it only exists in the second word. Consequently, 9XY is the greatest common monomial factor.
Although (b) 9Y⁴ is the closest response among the given possibilities, it is not our solution because (b) contains no X and Y appears at a higher power than in our largest common factor. Furthermore, since we are factoring rather than elevating terms to an exponent, we do not employ the cube operation. It is important to remember that cubing exponentials involves multiplying the exponent by three and cubing the numerical coefficient. However, we are factoring the terms in this problem instead of cubing them. As a result, (d) None of the above is the right response.