7.3 MULTIPLICATION AND EXPONENTS:

Base: A number that is multiplied repeatedly.

Exponent: A number that shows repeated multiplication.

Property: A character or attribute that something has.

GOAL:

Remember:An exponent equation has two

components:

𝑏𝑥

Base

Exponent

PROPERTIES: Multiplying powers withsame base:

For every number a≠0 and m, n, are integers,

= Ex:

1) 41 ∙ 43

2) 31 ∙ 3-3

= 41+3 = 256= 44 = = 31+-3 = 3-2 =

YOU TRY IT:

Simplify:

1) 124 12∙ -2

2) (-2)5 (-2)∙ -2

3) m3 m∙ -1 m∙ 5

4) 9-3 9∙ 2 9∙ -4

SOLUTION: No matter what integer it is, anything to the power of zero is 1.

1) 124 12∙ -2 124-2 122 144

2) (-2)5 (-2)∙ -2

3) m3 m∙ -1 m∙ 5

(-2)5-2 (-2)3 -8

4) 9-3 9∙ 2 9∙ -4

m3-1+5 m7 m7

9-3+2-4 9-5

PROPERTIES: Multiplying and Scientific notation

For every nonzero number a, b and integer n and m

(a×10n)(b×10m)=

a∙b×10n+m

EXAMPLE: Simplify:

1) (5×104)(12×10-2 )

2) (3×10-5)(4×10-2 )

3) (1.13×10-7)(9.8×105 )(3.34×1022)

SOLUTION: 1) (5×104)(12×10-2 )

2) (3×10-5)(4×10-2 )

3) (1.13×10-7)(9.8×105 )(3.34×1022)

(5)(12)× 104-2 60× 102 6.0× 103

(3)(4)× 10-5-2 12× 10-7 1.2× 10-6

(1.13)(9.8)(3.34)× 10-7+5+22

36.99× 1020 3.699× 1021

VIDEO:Get a hot chocolate

and enjoy this!!!.

http://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/negative-and-positive-exponents

PROPERTIES: ZERO: as an exponentFor every number a,

= 1Ex: 40 = 1 (-3)0 = 1 1000 = 1

1,000,0000 = 1 -½ 0 =-1

PROPERTIES: Negative numbers: as an exponents

For every nonzero number a≠0, and integer n

= 1) 4-1 = 2) (-3)-2 = Ex:

PROPERTIES: Multiplying powers withsame base:

For every number a≠0 and m, n, are integers,

= Ex:

1) 41 ∙ 43 = 41+3 = 44 = 2562) 31 ∙ 3-3 = 31+-3 = 3-2 = =

PROPERTIES: Multiplying and Scientific notation

For every nonzero number a, b and integer n and m

(a×10n)(b×10m)=

a∙b×10n+m

VIDEOS: Exponents and Multiplication

https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/rational-exponents-and-exponent-laws

https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/exponent-properties-involving-products

CLASSWORK:Page 424:

Problems: As many as needed to master the concept.

Page: 429:Problems: As many as needed

to master the concept.