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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.
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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
