Download Law of Exponents

WKSP
HW
Procedure
Media
Student Outcomes
Standard
Pre Requisite
Positive Exponents
Add Integers
8.EE.1 Know and apply the properties of integer exponents to generate equivalent
numerical expressions.
 Students know what it means for a number to be raised to a power and how to
represent the repeated multiplication symbolically.
 Students know the reason for some bases requiring parentheses.
 Students use the definition of exponential notation to make sense of the first law
of exponents.
 Students see a rule for simplifying exponential expressions involving division as a
consequence of the first law of exponents
 Students write equivalent numerical and symbolic expressions using the first law of
exponents.
https://www.youtube.com/watch?v=-NMph943tsw
Power of Love – Huey Lewis (Back to the Future)
http://www.math.harvard.edu/~knill/mathmovies/swf/diehard1.html
Die Hard III (rated R: language)
http://www.math.harvard.edu/~knill/mathmovies/swf/payitforward.html
Pay It Forward
http://www.math.harvard.edu/~knill/mathmovies/swf/startrek_spock.html
Star Trek (The Original Series) Episode 20: Court Martial
Law of Exponents
1. 𝑥 𝑚 ∙ 𝑥 𝑛 = 𝑥 𝑚+𝑛
#13
Spiral #3
Pascal’s Triangle
Positive Exponents
Express 3 + 3 + 3 + 3 + 3 by using multiplication
Exponential Notation
Express 3 x 3 x 3 x 3 x 3 by using an exponent:
9 4
What does (7) mean?
What is the value of 103?
BASEexponent
Exercise:
Rewrite the following using exponential notation.
1. 5 x 5 x 5 x 5 x 5 x 5 =
2. (-2) (-2) (-2) (-2) =
3.
2
5.
(3.8)(3.8)(3.8) =
3
2
2
2
x3x3x3=
Find the value of each expression:
2 2
7.
a. ( 3) =
b.
4
4
4
4.
(− 11) x (− 11) x (− 11) =
6.
(-2.01)(-2.01) =
22
3
=
8.
a. (-2)2 =
b. -22 =
9.
a. (-1)1 =
b. (-1)2 =
c. (-1)3 =
d. (-1)4 =
e. (-1)5 =
f. (-1)6 =
g. (-1)7 =
h. (-1)8 =
i. (-1)9 =
j. (-1)10 =
When a negative number is raised to an odd power, the sign of the result is __________.
When a negative number is raised to an even power, the sign of the result is _________.
What is the sign of the following?
10. (-5)95 =
11. (-1.8)122 =
Positive Exponents
Multiply Numbers in Exponential Form
52 x 54 is the same as 52 + 4 = 56
5x5x5x5x5x5
2 4
2 5
2 ?
This is true for all rational numbers! (− 3) × (− 3) = (− 3)
Law of Exponents
1. 𝑥 𝑚 ∙ 𝑥 𝑛 = 𝑥 𝑚+𝑛
Exercise: Show what needs to be done with the exponents. Then write an equivalent
value using a single exponent.
1.
1423 x 148 =
2.
(-72)10 x (-72)13 =
3.
a23 x a8 =
4.
Find x: (-3)9 x (-3)x = (-3)14
More than 2 terms that have the same base follows the same rule.
5. 94 x 96 x 913 =
6. 23 x 25 x 27 x 29 =
Be careful ……
Expressions can be simplified this way only when the bases are the ______.
In the expression 24 x 82, the bases are different. How can we get the bases to be the
same?
82 = = (2)
=2
So we really have 24 x 2 = 24 + = 2
Exercise: Write an equivalent expression using a single base and a single exponent.
7. 37 x 9 =
8. 24 ∙ 16 =
9.
53 (25) =
10. (4.2)5(17.64) =
Some terms cannot be brought together! If the bases cannot be the same, the bases
must stand alone!
54 x 211 =
65 x 49 x 43 x 614 =
Exercise: Write an equivalent expression using a single base and a single exponent.
Show all work.
11. (−4)2 ∙ 175 ∙ (−4)3 ∙ 177 =
12. 152 ∙ 72 ∙ 15 ∙ 74 =
Positive Exponents
13. 2 x 52 x 5-3 =
14. (3 x 103) ∙ (2 x 10-1) =
Name: __________________________________
Date: ______
Pre-Algebra
Exit Ticket
1.
Annie wrote (-3.1)(-3.1)(-3.1)(-3.1) = -3.14
Is Annie correct? Why or why not?
2.
Simplify by using a single exponent: 594 x 578
3.
Simplify as much as possible: 53 x 25
Positive Exponents
Name: _______________________________________
Pre-Algebra
Date: _____
HW #13
Lesson Summary

𝑥 𝑚 ∙ 𝑥 𝑛 = 𝑥 𝑚+𝑛
1. Rewrite each number in exponential notation using 2 as the base:
a. 8 =
b. 16 =
c. 32 =
d. 64 =
2. Tim wrote 16 as (-2)4. Is he correct?
3. Simplify by using a single exponent: (-3)9 x (-3)5 =
4. Simplify by using a single exponent: 32 x 3-5 =
Review:
Bob and Ray are describing the same number. Bob says, ‘The number is a positive
even integer less than or equal to 20.’ Ray says, ‘The number is divisible by 4.’ If
Bob’s statement is true and Ray’s statement is false, what are all the possible
numbers?