Powers and Exponents
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Transcript of Powers and Exponents
![Page 1: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/1.jpg)
Powers and
Exponents
![Page 2: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/2.jpg)
Multiplication = short-cut addition
When you need to add the same number to itself over and over again,
multiplication is a short-cut way to write the addition problem.
Instead of adding 2 + 2 + 2 + 2 + 2 = 10
multiply 2 x 5 (and get the same answer) = 10
![Page 3: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/3.jpg)
Powers = short-cut multiplication
When you need to multiply the same number by itself over and over again,
powers are a short-cut way to write the multiplication problem.
Instead of multiplying 2 x 2 x 2 x 2 x 2 = 32
Use the power 25 (and get the same answer) = 32
![Page 4: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/4.jpg)
A power =
a number written as
a base number with an exponent.
base exponent
Like this:
25 say 2 to the 5th power
![Page 5: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/5.jpg)
The base(big number on the bottom)=
the repeated factor in a multiplication problem.
base exponent = powerfactor x factor x factor x factor x factor = product
2 x 2 x 2 x 2 x 2 = 32
![Page 6: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/6.jpg)
The exponent (little number on the
top right of base) = the number of times the base is multiplied by itself.
25
2(1st time) x 2(2nd time) x 2(3rd time) x 2(4th time) x 2(5th time) = 32
![Page 7: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/7.jpg)
How to read powers and exponents
Normally, say “base number to the exponent number (expressed as ordinal number) power”
25 say 2 to the 5th power
Ordinal numbers: 1st, 2nd, 3rd, 4th, 5th,…
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squared = base2
22 say 2 to the 2nd power or two squared
MOST mathematicians say two squared
22 = 2 x 2 = 4
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cubed = base3
23 say 2 to the 3rd power or two cubed
MOST mathematicians say two cubed
23 = 2 x 2 x 2 = 8
![Page 10: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/10.jpg)
Common Mistake
25 ≠(does not equal) 2 x 5
25 ≠(does not equal)10
25 =2 x 2 x 2 x 2 x 2= 32
![Page 11: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/11.jpg)
Common Mistake
-24 ≠(does not equal)(-2)4
Without the parenthesis, positive 2 is multiplied by itself 4 times; then the answer is negative.
With the parenthesis, negative 2 is multiplied by itself 4 times; then the answer becomes positive.
![Page 12: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/12.jpg)
Common mistake
-24 = (-1)x(x means times) +24 =
-1 x +2 x +2 x +2 x +2 = -16Why?
The 1 and the positive sign are invisible.
Anything x 1=anything, so 1 x 2 x 2 x 2 x 2 = 16;
and negative x positive = negative
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Common Mistake
(-2)4= - 2 x -2 x -2 x -2 = +16Why? Multiply the numbers: 2 x 2 x 2 x 2 = 16 andthen multiply the signs: 1st negative x 2nd negative = positive; that positive x 3rd negative = negative; that negative x 4th negative = positive; so answer = positive 16
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When the exponent is 0,and the base is any number but 0, the answer is 1.
20 = 1
4,6380 = 1
Any number(except the number 0)0 = 1
00 = undefined
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When the exponent is 1,the answer is the same number as the base number.
21 = 2 4,6381 = 4,638any number1 = the same
base “any number”01 = 0
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The exponent 1 is
usually invisible.
![Page 17: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/17.jpg)
The invisible exponent 1
21 = 2 4,6381 = 4,638any number1 = the same base “any number”
01 = 0
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2 = 2 4,638 = 4,638any number = the same “any number” as the base
0 = 0The exponent 1 is here. Can you see it? It’s invisible. Or. It’s understood.
The invisible exponent 1
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“Write a power as a product…”
power = write the short-cut way
means 25 = 2 x 2 x 2 x 2 x 2
product = write the long way = answer
![Page 20: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/20.jpg)
“Find the value of the product…”
means answer
25 = 2 x 2 x 2 x 2 x 2 = 32
power = product = value of the product
(and value of the power)
![Page 21: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/21.jpg)
“Write prime factorization using exponents…”
125 = product 5 x 5 x 5 so
125 = power 53 = answer using exponents
product 5 x 5 x 5 = power 53
Same exact answer written two different ways.
![Page 22: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/22.jpg)
Congratulations!
Now you know how to write a multiplication problem as a product using factors, or as a power using exponents (this can be called exponential form).
You know how to (evaluate) find the value (answer) of a power.
![Page 23: Powers and Exponents](https://reader036.fdocuments.us/reader036/viewer/2022081420/56812cf7550346895d91c462/html5/thumbnails/23.jpg)
Notes for teachers
Correlates with Glencoe Mathematics (Florida Edition) texts:
Mathematics: Applications and Concepts Course 1: (red book)
Chapter 1 Lesson 4 Powers and ExponentsMathematics: Applications and Concepts Course 2:
(blue book) Chapter 1 Lesson 2: Powers and ExponentsPre-Algebra: (green book) Chapter 4 Lesson 2: Powers and ExponentsFor more information on my math class see http://
walsh.edublogs.org