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helpfulAnswer:
9x^2y^3Step-by-step explanation:
To find the greatest common factor (GCF) of these expressions, we need to find the largest factor that divides all three terms.
We can start by factoring each term into its prime factors:
27x^2y^3 = 3^3 * x^2 * y^3
45x^3y^4 = 3^2 * 5 * x^3 * y^4
9x^4y^3 = 3^2 * x^4 * y^3
To find the GCF, we need to look for the highest power of each prime factor that appears in all three terms. In this case, the highest power of 3 that appears in all three terms is 3^2, the highest power of x that appears in all three terms is x^2, and the highest power of y that appears in all three terms is y^3. Therefore, the GCF is:
GCF = 3^2 * x^2 * y^3 = 9x^2y^3
So the greatest common factor for the expressions 27x^2y^3, 45x^3y^4, and 9x^4y^3 is 9x^2y^3.
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