Warm Up I can simplify expressions with exponents. 1. What is the value of 3x 3 +2 when x=10? 2. You...
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Transcript of Warm Up I can simplify expressions with exponents. 1. What is the value of 3x 3 +2 when x=10? 2. You...
Warm UpI can simplify expressions with exponents.
1.What is the value of 3x3+2 when x=10?
2.You put $500 in an account that doubles every year.a.What is the equation for this
situation?
b.How much money would you have after 4 years?
𝟑𝟎𝟎𝟐
(x=years y=money)
𝒚=𝟓𝟎𝟎(𝟐)𝟒=$𝟖𝟎𝟎𝟎
Homework Questions
What an Exponent Represents
An exponent tells how many times a number is multiplied by itself.
34= 3 3 3 3= 81
How do you say this?
three to the third power
or
three cubed
3 3Base
Exponent
three to the 2nd power
Or
three squared
3 2Base
Exponent
How do you say this?
2. 8 8 8 8 =
Practice: Write in many different ways
1. 9 9 =
3. x x x x x =
4096
eight
x
Exponent Rules
𝑥𝑚 ∙ 𝑥𝑛=¿
Part 1
Product Rule:
𝒙𝒎+𝒏
Multiply same base, add the exponents
𝑥5 ∙𝑥3=𝑥8Example:
𝒙𝒎
𝒙𝒏 =¿
Part 2
Quotient Rule:
𝒙𝒎−𝒏
Divide same base, subtract the exponents
𝑥11
𝑥3 =𝑥8Example:
(𝒙 ¿¿𝒎)𝒏=¿ ¿
Part 3
Power Rule:
𝒙𝒎 ∙𝒏
Same base, multiply the exponents
(𝑥¿¿4 )2=𝑥8 ¿Example:
(𝒙𝒚 )𝒏=¿
Part 4
Expanded Power Rule:
(𝒙)𝒏¿
Apply outside exponent to all parts inside parenthesis
(3 𝑥¿¿ 4)2=32(𝑥4)2¿Example:
¿9 𝑥8
=
Part 5
Expanded Power Rule (cont):
( 𝑥2
𝑦 )4
=¿Example:
( 𝒙𝒏
𝒚𝒏 )Apply outside exponent to all
parts inside parenthesis
( 𝑥8
𝑦 4 )
(𝒙)𝟎=¿
Part 6
Zero Exponent Rule:
𝟏
Any base raised to 0 equals 1.
Example: 𝟏
NOTES
Negative ExponentsNegative exponents tell you how many times
you should divide by a number
Negative exponents move the base to bottom of a fraction
Note: the exponent becomes positive
Negative Exponents
25
1
5
12
Partners
Find a partner with a different letter
Compare and check each others answers
Worksheet
Complete any 10 problems
What’s the difference?
1)
2)
What’s the difference?
3)
4)