7-2: Division Properties of Exponents

7-2: Division Properties of Exponents

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.

•

•

4

732 2 2 2 2 2 2 2

2 2 2 2 22 2 2 2

3

4t t t tt t t t

t t

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

732

22 3

4tt

t

1111 8 3

8

c c cc

5

5 2 32

r r rr

7-2: Division Properties of Exponents

•Example 1: Simplify. Assume that x and y are not equal to zero▫

7 12 7 12

6 3 6 3

7 6 12 3

9

x y x yx y x y

x y

xy

1) Simplify

1 2 3 4

0%

89%

0%

11%

3 9

2

a bab

7

2

ba9

3 2a b

1. a4b11

2.

3.

4. a2b7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

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 4 4

4

3 35 5

5 5

5

r rt t

7-2: Division Properties of Exponents

•Example 2: Simplify. Assume that x and y are not equal to zero▫ 33 2 3 9 6

3

9 6

4 45 5

64125

c d c d

c d

2) Simplify

1 2 3 4

25% 25%25%25%

33 2

5

34m np q

9 6

15 3

2764m np q

9 6

15 3

34m np q

6 5

15

67m np q

6 3

8 4

2764m np q

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

1.

2.

3.

4.

7-2: Division Properties of Exponents

•Assignment▫Page 402-403▫1 – 11 & 19 – 29▫Odd problems only

7-2: Division Properties of ExponentsDay 2

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

08 7

5 10

12 18m nm n

7-2: Division Properties of Exponents

•Example 3: Simplify. Assume that m and n are not equal to zero▫ 0 3 3

2 2

m n nn n

n

3) Simplify

1 2 3 4

25% 25%25%25%

03 9

12

35x yz

1. 3/5

2. 1

3. 0

4. -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

4) Simplify

1 2 3 4

25% 25%25%25%

0 5

3

x kk

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

2kx

1. xk2

2.

3. (xk)2

4. k2

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 =

4

1 12 16

44

1 jj

7-2: Division Properties of Exponents

•Example 4: Simplify. Assume no denominator is zero▫ 4 9 9 6

6 4

x y y zz x

3 5 3 5

5 4 8 5 4 8

3 5 5 ( 4) 8

2 1 8

8

2

75 75 115 15

5

5

5

p q p qp q r p q r

p q r

p q r

rp q

5) Simplify

1 2 3 4

25% 25%25%25%

2 3

5

a bc

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

2 3

5

a bc

3 5

2

b ca

2 3 5a b c

5 2

3

c ab

1.

2.

3.

4.

6) Simplify

1 2 3 4

25% 25%25%25%

5 8 3

4 2 6

369x y zx y z

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

6

3

27xyz

6 3

4xy z

3

6

4zxy

6

3

4xyz

1.

2.

3.

4.

7-2: Division Properties of Exponents

•Assignment▫Page 402-403

13 – 17 31 – 41 45 - 55

▫Odd problems only