3 3 4 4 3 3 4 4 = = 3 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3
TRANSCRIPT
3344
3344== 33x 3x 3x 3x 3x 3x 3
==33 x 3x 3x 3x 3x 3x 3
Too many buttons!
AND… what if it is
something like 0.1279 25 ?
xyxy yxyx^̂
3344
== 8181
Communicate Your Understanding
MHR 113:C1, C2, C3, C4
Are these the same
thing?
Are these the same
thing?
-32-32 (-3)2(-3)2
=-(3x3)=-(3x3)
=-9=-9=(-3)(-3)=(-3)(-3)
=9=9
Page 120 #6PRODUCT Expanded Form Single Power
32 x 34
43 x 43
64 x 61
24 x 22 x 23
k3 x k5
Own example
(-2)3 x (-2)3
34
3
2
3
2
#9. Reflect: How can you write a product of powers using a single power?
Complete: #7, #8
#10. Write a rule for finding the product of powers.
xa x xb = xa+b
PRODUCT RULE x SHORTCUT
• Ensure same base!
• Add the exponents.
Apply the Product Rule(x shortcut)
a)
b)
c)
2421
5
2
5
2
330 77
243 222
Apply the product rule to write each as a single power. Evaluate the expression given in c)
Page 120 #11Quotient Expanded Form Single Power
55 53
74 71
106 104
27 26
p8 p5
Own example
(-2)5 x (-2)2
34
3
2
3
2
#14. Reflect: How can you write a quotient of powers using a single power?
Complete: #12, 13
#15. Write a rule for finding the quotient of powers.
xa xb = xa-b
QUOTIENT RULE SHORTCUT
• Ensure same base!
• Subtract the exponents.
Apply the Quotient Rule( shortcut)
a)
b)
c)
35
5
2
5
2
330 77
247 222
Apply the quotient rule to write each as a single power. Evaluate the expression given in b) and c)
Page 123 #1, 2, 3
Power of a Power
Expanded Form
Single Power
(22)3
(53)4
(104)2
245x
4229 y
32
3
1
#4. Write a rule for finding the power of a power.
(xa)b = xa x b
POWER OF A POWERSHORTCUT
• Multiply the exponents for each base in the brackets
Example Expanded Simplified Exponent Rule
Multiplication
Division
Power of Power Law
Power of a Product
Power of a Quotient
53 aa
2
6
a
a
42a
3ba
5
b
a
aaa aaaaa
aaaaaa aa
aa aaaaaa
ba ba ba
b
a
b
a
b
a
b
a
b
a
8a nm aa
n
m
a
a4a
8a nma
33ba mab
5
5
b
am
b
a
nma
nma
nma
mmba
m
m
b
a
nm aa nma
n
m
a
a nma
The bases must be the same!
Can you simplify
this?
Can you simplify
this?
nm aa
MHR textbook
p114 #5, #6, #8
p126: #1 through to #7
TIPS: p118 #17, #18