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How Do You Divide Monomials Using Quotient of Powers?

Find the quotient of 32a3b7c2 divided by 4ac4b5
Write your answer as a monomial in simplest form.

Summary

  1. Quotient means division
  2. 'a', 'b', and 'c' are variables
  3. Use the associative property to rearrange the denominator
  4. Split up the terms so that each term is being divided by a term with the same variable
  5. To divide two of the same variable, use the quotient of powers and just subtract their exponents

Notes

    1. The numerator is 32a3b7c2
    2. 'a', 'b', and 'c' are variables
    1. 'a', 'b', and 'c' are variables
    2. We just switch the c4 with the b5
    1. 'a', 'b', and 'c' are variables
    2. Now we have each variable in the numerator grouped with the same variable in the denominator
    1. We can cancel out the variables to simplify the quotient
    1. For now let's just rewrite 32/4
    1. To divide two of the same variable, use the quotient of powers and just subtract their exponents
    1. A negative power is the same as dividing by a positive power of the same value
    2. So dividing a3 by 'a' is the same as multiplying a3 by a-1
    3. And a3-1 is the same as dividing a3 by a
    4. 'a' is a variable
    1. A negative power is the same as dividing by a positive power of the same value
    2. So dividing b7 by b5 is the same as multiplying b7 by b-5
    3. And b7-5 is the same as dividing b7 by b5
    4. 'b' is a variable
    1. A negative power is the same as dividing by a positive power of the same value
    2. So dividing c2 by c4 is the same as multiplying c2 by c-4
    3. And c2-4 is the same as dividing c2 by c4
    4. 'c' is a variable
    1. 32 divided by 4 is 8
    2. a3-1 is just a2
    3. b7-5 is just b2
    4. c2-4 is just c-2
    5. c-2 is another way of writing 1 divided by c2
    6. 'a', 'b', and 'c' are variables