SWBAT… Multiply monomials Monday, 4/30

Agenda 1. WU (10 min)2. Lesson on multiplying monomials (3 slides & lots of ex) (35 min)

WU:

1. Write your HW in your planner2.

3.

4.

5. Set up notes: “Multiplying monomials”

22)5(

03 )2(32 d

29

Laws of Exponents

nmn

m

m

mm

mnnm

mmmnmnm

nnn

n

xx

x

y

x

y

x

xx

yxxyxxx

aa

anda

aa

.7.6

.5

.4.3

11.21.1 0

Product of Powers (3)Words: To multiply two powers that have the same base, add their exponents.

Symbols: For any real number x and any integer m and n, xmxn = xm + n

Examples

(x3)(x4) = x3+4 = x7

OR(x3)(x4) = (xxx)(xxxx)      = xxxxxxx            = x7

Examples

32 xx 32x 5x

675 xx 135x

73 26 nn

))(15( 67x

))(26( 73n 1012n

zabb zab

Examples

)8)(2( 3xyxy 4216 yx

612 yx))(( 3113 yxxy

cba xxx 82 cbax 16

))(( xyxy 22 yx

Power of a Power (4)Words: To raise a power to a power, multiply the exponents.

Symbols: For any real number x and any integers m and n, (xm)n = xm ∙ n

Examples:(x2)4 = x 2∙4 = x8

OR (x2)4 = (x2)(x2)(x2)(x2) = (xx)(xx)(xx)(xx) = x8     

(b3)5 = b3∙5 = b15

Examples

34x 34x 12x

232 ])3[( 232 )3( 26 )3(

123 441,531

524 524 104 576,048,1

Power of a Product (5)Words: If you have a product inside a parenthesis, and a power on the parenthesis, then the power goes on each coefficient and each variable inside (“distribute” the exponent to each coefficient and/or variable.)

Symbols: For any real number x and any integer m, (xy)m = xmym

Examples (xy)3 = x3y3

OR (xy)(xy)(xy) = (xxx)(yyy) = x3y3

Examples (cont’d)

53)2( xy 5)3(55)2( yx

15532 yx

32xy 63yx

232 ])4[( 12)4( 216,777,16

Examples

638 )2()5( xyyx ))2)((5( 6663243 yxyx 9308000 yx

)2()2( 343 xyxy )2()2( 31244 xyyx

15532 yx