# Dividing Powers and Monomials

There are 3 procedures that must be followed in order to divide powers and

monomials. Providing that the powers having the same base  They are:

1) Numerator is larger than the exponent of the denominator

2) Exponents are equal

3) Exponent of the denominator is larger

Rule 1) If the exponent of the numerator is larger than the exponent of the

numerator. The following procedure is applied:

a) Arrange them like a fraction

b) The base remains the same

c) Subtract the smaller exponent from the larger.

Example:

y8/y4

y8-4= y4

Example 2

x5/x3 = X5-3 = x2

Rule 2

If the exponents are equal, we then follow the same previous procedure, as

a) Arrange them like fraction

b) Base remains the same, or divide by itself

c) As a result the quotient is equal to one.

Example

y2/y2 = 1

x3/x3 = 1

Rule 3

What if the exponent of the denominator is larger than the numerator. In this case,

we have the following.

1) Make the numerator of the quotient equal to 1

2) The base remains the same.

3) Subtract the smaller exponent from the larger.

Example

x3/x5 = 1/x5-3 = 1/x2

y4/y6

As a result, we now have.

1/y6-4 = 1/y2