7.4 multiplication and exponents:
DESCRIPTION
Base: A number that is multiplied repeatedly. 7.4 MULTIPLICATION AND EXPONENTS:. Exponent: A number that shows repeated multiplication. Property: A character or attribute that something has. GOAL:. Remember:. An exponent equation has two components:. Exponent. Base. - PowerPoint PPT PresentationTRANSCRIPT
7.4 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: Raising powers to powers:
For every number a≠0 and m, n, are integers,
= Ex:
1) (41)3 2) (31)-3
= 41∙3 = 43 = 64= = 31 ∙ -3 = 3-3 =
YOU TRY IT: Simplify:
1) (124)-2
2) ((-2)5)-2
3) (m3 )-1 m∙ 5
4) (9-3 )2 9∙ -4
SOLUTION: No matter what integer it is, anything to the power of zero is 1.
1) (124)-2 12(4)(-2) 12-8
2) ((-2)5)-2
3) (m3)-1 m∙ 5
(-2)(5)(-2) (-2)-10
4) (9-3)2 9∙ -4
m(3)(-1)+5 m-3+5 m2
9(-3)(2)-4 9-10
PROPERTIES: Raising a product to powers:
For every number a≠0 and m, n, are integers,
= Ex:
1) (4x)3
2) (3s)-3
= 43x3 = 64x3 = 3-3s-3 = =
YOU TRY IT: Simplify:
1) (12y)-2
2) (-2c)5
3) (mz)3 m∙ 5
4) (9-3 n)2 9∙ -4
SOLUTION: No matter what integer it is, anything to the power of zero is 1.
1) (12y)-2 12-2y-2
2) (-2c)5
3) (mz)3 m∙ 5
(-2) 5c5 -32c5
4)(9-3z)2 9∙ -4
m3z3m5 m3+5z3 m8z3
9(-3)(2) z2 9∙ -4 9-10 z2
PROPERTIES: Multiplying and Scientific notation
For every nonzero number a, b and integer n and m
(a×10n)c(b×10m)=
ac∙b×10(n)(c)+m
EXAMPLE: Simplify:
1) (5×104)3(6×10-2 )
2) (3×10-5) 3(4×10-2 )
3) (1.13×10-7)3(9.8×105 )(3.34×1022)
SOLUTION: 1) (5×104)3(6×10-2 )
2) (3×10-5)3(4×10-2 )
3) (1.13×10-7)3(9.8×105 )(3.34×1022)
(53)(6)× 10(4)(3)-2 750× 1010 = 7.50×1012
(33)(4)× 10(-5)(3)-2 108× 10-17 1.08×10-15
(1.133)(9.8)(3.34)× 10(-7)(3)+5+22
47.23× 106 4.723× 107
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
VIDEO:Raising a Power to a Power
WithExponents
http://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/exponent-properties-3
CLASSWORK:
Page 436-437:
Problems: As many as neededto master the concept