Copyright©amberpasillas2010. Simplify two different ways. == = =

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

=


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

=


Just Subtract the Exponents!

Your short cut is called the

Quotient of Powers Property.

7

4

x

x

7 4x 3x


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!”


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


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


Simplify Using What You Just Learned.11

8101) 10

11 810 310

1000

15

7x2) x

15 7x 8x


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


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.


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.


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


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



3 42x 5x 10 3 4 x 7 10x



210y 5y 50 2 1 y 3 50y


2(7ab)(2a )

14

1) 2) 2 4 7(2xy )( 3x y )

6

Simplify.

3a b 5x 9y


7 2

410m n

2m n102

7 4m 2 1n

5 3m 1n

5 3m

1

n


9 6

480a n100a n

80100

9 4a 6 1n

80100

5a 5n2020

45

5a 5n


2 315x y

12xy

3

3

5

4

2 25xy

4

1


8 5

3 2

30a b

42a b

6

6

5

7

55 35a b

7

3


Take Out Your Study Guide!!!


# 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


#17

2 315x y12xy

1512

2 1x 3 1y

54x 2y

2 315x y

12xy

3

3

5

4

21

25xy

4



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

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