copyright©amberpasillas2010. simplify two different ways. == = =
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copyright©amberpasillas2010
copyright©amberpasillas2010
Simplify two different ways.410m
15m=
2 5 m m m m 3 5 m =
32m
3
4 110m
15
=410m
15m32
m3
=
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How do you divide expressions with exponents?
Ex: a5 a3 Let’s look at
each problem in factored form.
a • a • a • a • a a • a • a
x • x • x • x x • x
Notice that youcan cancel from numerator to denominator.
= a2
= x2
Do you see a “shortcut” for dividing these expressions?
4
2
x
x
=
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Just Subtract the Exponents!
Your short cut is called the
Quotient of Powers Property.
7
4
x
x
7 4x 3x
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Simplify.
x 5
x 2 =x x x x x
x x = x x x 3x
x 5
x 2 =5 2x 3x
Quotient of Powers Propertyx a
x b =a bx
or “When you divide powers,
you subtract the exponents!”
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Simplify.
5 5 5 5 5 5 5 5 5 5
56
=54 5
6 - 4
=
= 52
52
Quotient of Powers Propertyx a
x b =a bx
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Simplify Using What You Just Learned.
1)
3)
2)
4)
4
3
x
x6
3
k
k
5
2
9
3
m
m
9
3
4
2
x
x
1x
3k
33m
62x
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Simplify Using What You Just Learned.11
8101) 10
11 810 310
1000
15
7x2) x
15 7x 8x
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Simplify Using What You Just Learned.14
1273) 7
14 127 27
49
3 13
6a b c4) ab3 1a
2 7a b c
13 6b c
1
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Power to Power Rule
( )xa
=b
xab
( )23
=-2
23(-2)
= 2-6
= 6
1
2=
1
64
( )8-2
= 2
1
8=
1
64
Negative exponents follow rules of exponents.
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Simplify in two different ways.5
4x
x 5 4 x 9 x
5 4x x 4
5 x 1
1x
5 4 x x
1 1
1 1 9 x
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction.
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Simplify in two different ways.4 3 y y
43
1yy
4
3
yy
y y y yy y y y
4 3y y 1
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COEFFICIENT: The number in front of the variable is the coefficient. Multiply coefficients. Add exponents if the bases are the same
3 52x 4x 8 3 5 x 8 8x
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COEFFICIENT: The number in front of the variable is the coefficient. Multiply coefficients. Add exponents if the bases are the same
3 42x 5x 10 3 4 x 7 10x
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COEFFICIENT: The number in front of the variable is the coefficient. Multiply coefficients. Add exponents if the bases are the same
210y 5y 50 2 1 y 3 50y
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2(7ab)(2a )
14
1) 2) 2 4 7(2xy )( 3x y )
6
Simplify.
3a b 5x 9y
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7 2
410m n
2m n102
7 4m 2 1n
5 3m 1n
5 3m
1
n
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9 6
480a n100a n
80100
9 4a 6 1n
80100
5a 5n2020
45
5a 5n
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2 315x y
12xy
3
3
5
4
2 25xy
4
1
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8 5
3 2
30a b
42a b
6
6
5
7
55 35a b
7
3
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Take Out Your Study Guide!!!
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# 16When Dividing Powers with the same base,
just SUBTRACT THE EXPONENTS. This is called the
Quotient of Powers Property.
x 5
x 2 =x x x x x
x x = x x x 3x
x5
x 2 =5 2x 3x
or
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#17
2 315x y12xy
1512
2 1x 3 1y
54x 2y
2 315x y
12xy
3
3
5
4
21
25xy
4
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COEFFICIENT: The number in front of the variable is the coefficient. Multiply coefficients. Add exponents if the bases are the same
3 52x 4x 8 3 5 x 8 8x
# 18
2(7ab)(2a )
14
1) 2) 2 3 4(2x y )( 3x y)
63a b 6x 4y