1. 7-2: Division Properties of Exponents

2. 7-2: Division Properties of Exponents
You can use repeated multiplication to simplify fractions. Expand the numerator and denominator using repeated multiplication. Then cancel like terms.

3. 7-2: Division Properties of Exponents
Note that 7 – 4 = 3, and 4 – 3 = 1
Quotient of Powers
To divide two powers that have the same base, subtract the denominator exponent from the numerator exponent.
Examples

4. 7-2: Division Properties of Exponents
Example 1: Simplify. Assume that x and y are not equal to zero

5. 1) Simplify
a4b11
a2b7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

6. 7-2: Division Properties of Exponents
Power of a quotient
Just like with multiplication, when an exponent is on the outside of parenthesis, multiply exponents
Examples

7. 7-2: Division Properties of Exponents
Example 2: Simplify. Assume that x and y are not equal to zero

8. 2) Simplify 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

9. 7-2: Division Properties of Exponents
Assignment
Page
1 – 11 & 19 – 29
Odd problems only

10. 7-2: Division Properties of Exponents
Day 2

11. 7-2: Division Properties of Exponents
Zero Exponent Property
Any nonzero number raised to a zero power is equal to 1
Examples
150 = 1
(b/c)0 = 1
(2/7)0 = 1

12. 7-2: Division Properties of Exponents
Example 3: Simplify. Assume that m and n are not equal to zero

13. 3) Simplify
3/5 1 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

14. 4) Simplify
xk2
(xk)2 k2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

15. 7-2: Division Properties of Exponents
Negative Exponent Property
Negative exponents mean move the base to the other side of a fraction, and turn the exponent positive
Examples
2-4 =

16. 7-2: Division Properties of Exponents
Example 4: Simplify. Assume no denominator is zero

17. 5) Simplify 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

18. 6) Simplify 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

19. 7-2: Division Properties of Exponents
Assignment
Page
13 – 17
31 – 41
Odd problems only