Embed Size (px)
Citation preview
! 1!Algebra(I(Unit(3(Exponential(and(Quadratic(Relationships(
Chapter(7(Exponents(and(Exponential(Functions(
Lesson(7>1(Multiplication(Properties(of(Exponents(Objectives:! I!can!multiply!monomials!using!the!properties!of!exponents.!! ! I!can!simplify!expressions!using!the!multiplication!properties!of!exponents.!CCSS:! ! A.SSE.2,!F.IF.8b,!MP.8!
!Example(1:((Identify(Monomials(
Determine!whether!each!expression!is!a!monomial.!!Write!yes!or!no.!!Explain!your!reasoning.!
a. 17!–!c!!
b. !!
c. !!
d. !(
Guided(Practice(1:(Identify(Monomials(
Determine!whether!each!expression!is!a!monomial.!!Write!yes!or!no.!!Explain!your!reasoning.!
a. –x!+!5!!
b. !!
c. !!
d. !!
(Example(2:((Product(of(Powers(
Simplify!each!expression.!
a. (!
b. (!
€
8 f 2g
€
34
€
5t
€
23abcd2
€
xyz2
2
€
mpn
€
(r4 )(−12r7)
€
(6cd5)(5c5d2)
No
Yes
; No
s !
yes !
@ 0 =-Rr4t7= - Rr
"
#-00 =soidt
! 2!Guided&Practice&2:&Product&of&Powers&
Simplify!each!expression.!
a. &!
b. &&
&Standardized&Test&Example&3:&&Power&of&a&Power&
Simplify! .!
A!! ! ! B!! ! ! C!! ! ! D!! !
& & & &
Guided&Practice&3:&Power&of&a&Power&
Simplify! .!
F!! ! ! G!! ! ! H!! ! ! J!! !
& & & &
&Example&4:&&Power&of&a&Product&
Express!the!volume!of!a!cube!with!side!length!5xyz!as!a!monomial.!&
&
&
€
(3y4)(7y5)
€
(−4rx2t3)(−6r5x2t)
€
23" # $ %
& ' 3(
) *
+
, - 2
€
82
€
84
€
211
€
218
€
22" # $ %
& ' 2(
) *
+
, - 4
€
28
€
210
€
216
€
224
U u=2ly9
=Z4r6x4E'
(e) 3×2*2×2
×"
✓✓ 18 3.3=9
g. 2=182
O2.2=4
4.4.16
0
T
wasE#sns3
V=(5xyz )
53×393-23=125×33-23
! 3!Guided&Practice&4:&&Power&of&a&Product&
a. Express!the!area!of!a!square!with!sides!of!length! !as!a!monomial.!
!
b. Express!the!area!of!a!triangle!with!height!4a!and!base! !as!a!monomial.!
!!!
!Example&5:&&Simplify&Expressions&
Simplify! .!
!!!Guided&Practice&5:&&Simplify&Expressions&
Simplify! .!
!
&Lesson&7=2&Division&Properties&of&Exponents&Objectives:! I!can!divide!monomials!using!the!properties!of!exponents.!! ! I!can!simplify!expressions!containing!negative!and!zero!exponents.!CCSS:! ! A.SSE.2,!F.IF.8b,!MP.2!!
&
&
€
3xy2
€
5ab2
€
8g3h4" # $ %
& ' 2(
) *
+
, - 22gh5" # $ %
& ' 4
€
12a2b2
"
# $
%
& ' 3
−4b( )2) * +
, - . 2
9 ×2y4Azs2 (3×5)
?
= 32×2:A=tzbh }(5ab2)(4a)= 10dB
My qziegllehle
(IT §4g'2h16 ) 12494ha) 164g' 6h36
¥ £8424g
16h36 -7
Easy"
Kayani)4÷aW@a@
! 4!Example(1:((Quotient(of(Powers(
Simplify! .!!Assume!that!no!denominator!equals!zero.!
( ( ( ( (
(
Guided(Practice(1:(Quotient(of(Powers(
Simplify!each!expression.!!Assume!that!no!denominator!equals!zero.!
a. !
!
b. !
!
!Example(2:((Power(of(a(Quotient(
Simplify! .!!!
( ( (
( ( ( (
Guided(Practice(2:((Power(of(a(Quotient(
Simplify!each!expression.!
((a.( 5x5y6
!
"#
$
%&
2
( ( ( ( ( ( b.!! 2y2
3z3!
"#
$
%&
2
!
(
€
x7y12
x6y3
€
x3y4
x2y
€
k7m10pk5m3p
€
4c3d2
5
"
# $ $
%
& ' '
3
xtuy' "
= ×y9
=x "y "
= xy3
poet
= kt5mio→pI=K2m7
9=43;D = beat
⇒eye EID II25*105236
! 5!
!
Example!3:!!Zero!Exponent!
Simplify!each!expression.!!Assume!that!no!denominator!equals!zero.!
a. !
!
b. !
! ! ! !
! ! ! ! ! !
Guided!Practice!3:!Zero!Exponent!
Simplify!each!expression.!!Assume!that!no!denominator!equals!zero.!
a. !
!
b. !
!
!
€
12m8n7
8m5n10"
# $ $
%
& ' '
0
€
m0n3
n2
€
b4c2d0
b2c
€
2 f 4g7h3
15 f 3g9h6"
# $ $
%
& ' '
0
: 1
M
= n
A=
b4'it 1=@
= 1
! 6!Example(4:((Negative(Exponents(
Simplify!each!expression.!!Assume!that!no!denominator!equals!zero.!
a. (
!
!
b. (
( ( (
( ( ( ( ( ( (
Guided(Practice(4:(Negative(Exponents(
Simplify!each!expression.!!Assume!that!no!denominator!equals!zero.!
a. (
(
(
b. (
(
(
c. (
(
(Lesson(7=3(Rational(Exponents(Objectives:! I!can!evaluate!and!rewrite!expressions!involving!rational!exponents.!! ! I!can!solve!equations!involving!expressions!with!rational!exponents.!CCSS:! ! N.RN.1,!N.RN.2,!MP.5!
(
€
x−4y9
z−6
€
75p3m−5
15p5m−4r−8
€
v−3wx2
wy−6
€
32a−8b3c−4
4a3b5c−2
€
5 j−3k2m−6
25k−4m−2
= ¥26
Nt Fri
p=xy@
a3++8¥@
= EEK : ¥t€
! 7!!Example!1:!!Radical!and!Exponential!Forms!Write!each!expression!in!radical!form,!or!write!each!radical!in!exponential!form.!
a. !b. !
c. !d. !
!
Guided!Practice!1:!Radical!and!Exponential!Forms!Write!each!expression!in!radical!form,!or!write!each!radical!in!exponential!form.!
a. !
b. !
c. !d. !
!
!!Example!2:!!nth!roots!Simplify.!
a. ! ! ! ! ! b.!!!! 15,6256 !!
!
Guided!Practice!2:!nth!roots!Simplify.!
a. ! ! ! ! ! b.!!! 100004 !!
€
8112
€
38
€
12m12
€
32w
€
22
€
a12
€
(7w)12
€
2 x
€
2564
€
643
= if= 3842
IZTM
= ( 32W )k ÷ 32kWh
=zzY2
:Fwzxk
=25614
4*4=40 at -f5DId@
4 = 10
! 8!
!
Example(3:((Evaluate( (Expressions(Simplify.!
a. ! ! ! ! ! b.!!! 240114 !
!
Guided(Practice(3:(Evaluate( (Expressions(Simplify.!
a. ! ! ! ! ! b.!!!! 25614 !
!
!
Example(4:((Evaluate( (Expressions(
Simplify.!
a. ! ! ! ! ! b.!8152 !
!
Guided(Practice(4:(Evaluate( (Expressions(Simplify.!
a. ! ! ! ! ! b.!! 25654 !
!
€
b1n
€
133113
€
b1n
€
2713
€
bmn
€
3225
€
bmn
€
2723
( YK}z2)' ' 5 §l"§22=4 (9)5.59049€
(zzt3)2 q ( 256"D532=4 (4) 5=1024
! 9!
!
Example!5:!!Solve!Exponential!Equations!
Solve!each!equation.!
a. !!
b. !!
!
Guided!Practice!5:!!Solve!Exponential!Equations!
Solve!each!equation.!
a. !!
!
b. !!
!
!Real:World!Example!6:!!Solve!Exponential!Equations!The!population!p!of!a!culture!that!begins!with!40!bacteria!and!doubles!every!8!hours!can!be!modeled!by!
,!where!t!is!time!in!hours.!!Find!t!if!p!=!20,480.!!!!!!Guided!Practice!6:!!Solve!Exponential!Equations!
The!radius!r!of!the!nucleus!of!an!atom!of!mass!number!A!is! !femtometers.!!Find!A!if!r!=!3.6!femtometers.!!
€
9x = 729
€
162x−1 = 8
€
5x = 125
€
122x+3 = 144
€
p = 40(2)t8
€
r = 1.2(A)13
9¥93#
z4C2*D=23 ytqzxD= 3
sxtt,=L , sexist×=@
! 10!Lesson&7(4&Scientific&Notation&Objectives:! I!can!express!numbers!in!scientific!notation.!! ! I!can!find!products!and!quotients!of!numbers!expressed!in!scientific!notation.!CCSS:! ! A.SSE.2,!MP.3,!MP.6!
!
&
Example&1:&&Standard&Form&to&Scientific&Notation&Express!each!number!in!scientific!notation.!
a. 4,062,000,000,000!!
b. 0.000000823!&
Guided&Practice&1:&Standard&Form&to&Scientific&Notation&Express!each!number!in!scientific!notation.&
a. 68,700,000,000&!
b. 0.0000725&
&Example&2:&&Scientific&Notation&to&Standard&Form&Express!each!number!in!standard!form.!
a. 6.49!x!
€
105&
&
b. 1.8!x!
€
10−3&
-- -
- -
•4.062×1012
IT 8.23
•0018
! 11!Guided&Practice&2:&Scientific&Notation&to&Standard&Form&
Express!each!number!in!standard!form.!
a. 3.201!x!
€
106&
&
b. 9.03!x!
€
10−5 &
&
&Example&3:&Multiply&with&Scientific&Notation&
Evaluate!
€
5 ×10−6( ) 2.3 ×1012( ) .!!Express!the!result!in!both!scientific!notation!and!standard!form.!&&&&Guided&Practice&3:&Multiply&with&Scientific&Notation&
Evaluate!each!product.!!Express!the!results!in!both!scientific!notation!and!standard!form.!
a.
€
6.5 ×1012( ) 8.7 ×10−15( ) &!
b.
€
7.8 ×10−4( )2 &&
&Example&4:&Divide&with&Scientific&Notation&
Evaluate!
€
4.5 ×108
1.5 ×1010.!!Express!the!result!in!both!scientific!notation!and!standard!form.!
&&&&Guided&Practice&4:&Divide&with&Scientific&Notation&Evaluate!each!quotient.!!Express!the!results!in!both!scientific!notation!and!standard!form.!
a.
€
2.3958 ×103
1.98 ×108&
!
b.
€
1.305 ×103
1.45 ×10−4&
imwzz0@
•O0O090#•(000005 ) (
2,300,000,000¥ (5) (2-3)×-156+124500,000 1.15×107 B.5×100+1
I. 15×107 11500000
g
;@ao⇒X( 0-5.0000/21
.9×107 9×106
! 12!Real%World*Example*5:*Use*Scientific*Notation*
Last!year!Ally’s!state!registered!over!400!thousand!watercraft.!!Boat!sales!in!her!state!generated!more!than!$15.4!million!in!state!sales!taxes!that!same!year.!
a. Express!the!number!of!watercraft!registered!and!the!state!sales!tax!generated!from!boat!sales!last!year!in!Ally’s!state!in!standard!notation.!
!
b. Write!each!number!in!scientific!notation.!
!
c. How!many!watercraft!have!been!registered!in!Ally’s!state!if!12!times!the!number!registered!last!year!have!been!registered!in!all?!!Write!your!answer!in!scientific!notation!and!standard!form.!
***Guided*Practice*5:*Use*Scientific*Notation*
Suppose!a!satellite!radio!company!earned!$125.4!million!in!one!year.!
a. Write!this!number!in!standard!form.!
!
b. Write!this!number!in!scientific!notation.!
!
c. If!the!following!year!the!company!earned!2.5!times!the!amount!earned!the!previous!year,!determine!the!amount!earned.!!Write!your!answer!in!scientific!notation!and!standard!form.!
*!
*Lesson*7%5*Exponential*Functions*
Objectives:! I!can!graph!exponential!functions.!! ! I!can!identify!data!that!display!exponential!behavior!CCSS:! ! F.IF.7e,!F.LE.2,!MP.1!
*
****
400,000↳
15,400,000=
4×105 1,54×107
r (4×05)=48×105 =4g8go×do0@
125,400,000
1.254×108
2.5 (1.254×108) = 3.135×108
313,500,000
