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How Do You Multiply Quotients of Monomials?

Find the product of the two rational expressions shown on the right.

Summary

  1. Multiply the numerators together
  2. 2x2y times 9y2z equals 18x2y3z
  3. Then multiply the denominators together
  4. 3yz times 16xd2 equals 48xyzd2
  5. GCF stands for greatest common factor
  6. The GCF is the product of all the common factors between the numerator and denominator
  7. Since the GCF is in both the numerator and denominator, we can just divide each one by the GCF to find our answer

Notes

    1. The numerators are the top parts of the fractions, 2x2y and 9y2z
    1. We are multiplying the numerators together, which happen to be monomials
    1. The denominators are the bottom parts of the fractions, 3yz and 16xd2
    1. We are multiplying the denominators together, which happen to be monomials
    1. GCF stands for greatest common factor
    1. The product of all the common factors between the numerator and denominator will give us our GCF
    2. GCF stands for greatest common factor
    1. 18 = 3 • 3 • 2
    2. 48 = 3 • 2 • 2 • 2 • 2
    3. There is one 3 and one 2 in both 18 and 48, so their common factor is 3 • 2 = 6
    1. x = x
    2. x2 = x • x
    3. There is one x in both x and x2, so their common factor is just x
    1. y = y
    2. y3 = y • y • y
    3. There is one y in both y and y3, so their common factor is just y
    1. Since there is no common factor involving 'd' it is not part of the GCF
    2. GCF stands for greatest common factor
    1. GCF stands for greatest common factor
    1. GCF stands for greatest common factor
    1. The numerator is 18x2y3z
    2. We are dividing by 6xyz
    1. GCF stands for greatest common factor
    1. We divided 18x2y3z by 6xyz
    2. 18/6 = 3
    3. x2/x = x
    4. y3/y = y2
    5. z/z = 1
    1. The denominator is 48xyzd2
    2. We are dividing by 6xyz
    1. GCF stands for greatest common factor
    1. We divided 48xyzd2 by 6xyz
    2. 48/6 = 8
    3. x/x = 1
    4. y/y = 1
    5. z/z = 1
    1. Since we have divided the numerator and denominator by their GCF, we have simplified them as much as possible
    2. GCF stands for greatest common factor
    1. Since we have divided the numerator and denominator by their GCF, we have simplified them as much as possible
    2. GCF stands for greatest common factor
    1. Since we have divided the numerator and denominator by their GCF, we have simplified them as much as possible
    2. GCF stands for greatest common factor
    3. The simplified numerator is 3xy2 and the simplified denominator is 8d2