**Division of Monomials**

When one variable is divided by another variable with the same base, the exponent of the variable in the denominator is subtracted from the exponent of the variable in the numerator. For example,

*In general* ,

**Example 1**

Divide x ^{5} by x ^{3} .

**Solution 1**

*To divide a monomial by a monomial, divide the numerical coefficients and then subtract the exponents of the same variables* .

**Examples**

**Example 2**

Divide 15x ^{5} by -5x ^{3} .

**Solution 2**

**Example 3**

Divide 12x ^{4} y ^{6} by 3xy ^{4} .

**Solution 3**

**Math Note:** x ^{0} = 1 (x ≠ 0).

**Example 4**

Divide 18x ^{3} y ^{2} z ^{4} by 3xy ^{2} z ^{3} .

**Solution 4**

**Division of Monomials Practice Problems**

**Practice**

Divide:

1. 36m ^{3} n ^{4} ÷ 9m ^{2} n

2. -40x ^{5} y ^{4} z ^{5} ÷ 8x ^{3} y ^{2} z ^{2}

3. 15a ÷ 3

4. 49a ^{4} b ^{5} (-7ab ^{4} )

5. -21c ^{4} d ^{2} (-7cd)

**Answers**

1. 4mn ^{3}

2. -5x ^{2} y ^{2} z ^{3}

3. 5a

4. -7a ^{3} b

5. 3c ^{3} d

Practice problems for these concepts can be found at: Operations With Monomials And Polynomials Practice Test.

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