1. Monomial Division

2. Example 1
Divide 𝑥 7 by 𝑥 2 .
Use the rules of exponents to simplify the quotient of the powers of the same base: subtract the exponents.
𝑥 7 𝑥 2 = 𝑥 7−2 = 𝑥 5

3. Practice Problem 1 Divide 𝑎 9 by 𝑎 4 .
Use the rules of exponents to simplify the quotient of the powers of the same base.
𝑎 9 𝑎 4 = 𝑎

4. Example 2
Divide 𝑎 5 𝑏 6 by 𝑎 4 𝑏 3 .
Use the rules of exponents to simplify the quotient of the powers of the same base: subtract the exponents.
Do not combine powers of different bases.
𝑎 5 𝑏 6 𝑎 4 𝑏 3 = 𝑎 5−4 𝑏 6−3 = 𝑎 1 𝑏 3 =𝑎 𝑏 3

5. Practice Problem 2 Divide 𝑝 8 𝑞 9 by 𝑝 2 𝑞 7 .
Use the rules of exponents to simplify the quotient of the powers of the same base.
Do not combine powers of different bases.
𝑝 8 𝑞 9 𝑝 2 𝑞 7 = 𝑝 𝑞

6. Example 3
Divide 12𝑚 10 𝑛 7 by 3 𝑚 3 𝑛 5 .
Cancel out the Greatest Common Factor (GCF) of the numerical coefficient.
GCF of 12 and 3 is 3; 12 ÷ 3 = 4. 
Use the rules of exponents to simplify the quotient of the powers of the same base.
12 𝑚 10 𝑛 7 3𝑚 3 𝑛 5 =4 𝑚 10−3 𝑛 7−5 = 4𝑚 7 𝑛 2

7. Practice Problem 3 Divide 24𝑥 7 𝑦 11 by 8 𝑥 4 𝑦 6 .
Cancel out the Greatest Common Factor (GCF) of the numerical coefficients.
GCF of 24 and 8 is ; 24 ÷ =   .
Use the rules of exponents to simplify the quotient of the powers of the same base.
24 𝑥 7 𝑦 𝑥 4 𝑦 6 = 𝑥 𝑦

8. Practice Problem 4 Divide 28𝑎 6 𝑏 7 𝑐 4 by 7 𝑎 6 𝑏 𝑐 2 .
Cancel out the Greatest Common Factor (GCF) of the numerical coefficients.
GCF of 28 and 7 is ; 28÷ =  .
Use the rules of exponents to simplify the quotient of the powers of the same base
Recall that 𝑎 0 =1 and 𝑏 1 =𝑏.
28 𝑎 6 𝑏 7 𝑐 4 7𝑎 6 𝑏𝑐 2 = 𝑏 𝑐

9. Exercises
1. 𝑧 12 𝑧 𝑡 10 5𝑡 𝑎 6 𝑏 11 9𝑎 5 𝑏 𝑥 8 𝑦 13 𝑧 4𝑥 2 𝑦 5. 20𝑝 4 𝑞 7 𝑟 12 2𝑝𝑞 7 𝑟 4

10. Answer Key
Practice Problems 1. 𝑎 9 𝑎 4 = 𝑎 9−4 = 𝑎 5 2. 𝑝 8 𝑞 9 𝑝 2 𝑞 7 = 𝑝 8−2 𝑞 9−7 = 𝑝 6 𝑞 2 3. GCF of 24 and 8 is 8; 24 ÷ 8 = 𝑥 7 𝑦 11 8𝑥 4 𝑦 6 = 3𝑥 7−4 𝑦 11−6 =3 𝑥 3 𝑦 5 4. GCF of 28 and 7 is 7, 28 ÷ 7 = 𝑎 6 𝑏 7 𝑐 4 7𝑎 6 𝑏𝑐 2 = 4𝑎 6−6 𝑏 7−1 𝑐 4−2 =4 𝑏 6 𝑐 2

11. Answer Key Continued Exercises 1. 𝑧 12 𝑧 7 = 𝑧 12−7 = 𝑧 5
1. 𝑧 12 𝑧 7 = 𝑧 12−7 = 𝑧 5
𝑡 𝑡 4 =5 𝑡 10−4 =5 𝑡 6
𝑎 6 𝑏 𝑎 5 𝑏 9 =4 𝑎 6−5 𝑏 11−9 =4𝑎 𝑏 2
4. 8𝑥 8 𝑦 13 𝑧 4𝑥 2 𝑦 =2 𝑥 8−2 𝑦 13−1 𝑧=2 𝑥 6 𝑦 12
𝑝 4 𝑞 7 𝑟 𝑝𝑞 7 𝑟 4 =10 𝑝 4−1 𝑞 7−7 𝑟 12−4 =10 𝑝 3 𝑟 8