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For Learning to Happen!
•Remove all other thoughts from your mind.•Pay close attention to this lesson.•Try all of the examples.•Ignore all other distractions.
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An exponent is a little number high and An exponent is a little number high and to the right of a regular or base number.to the right of a regular or base number.
83
BaseExponent
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83
BaseExponent
This exponent is read This exponent is read
8 to the 3rd power, 8 to the 3rd power,
or 8 cubed.or 8 cubed.
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83
BaseExponent
An exponent tells how An exponent tells how many times a number is many times a number is multiplied by itself. multiplied by itself.
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83
BaseExponent
This exponent means This exponent means
8•8•8 = 512
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This exponent is read This exponent is read
six to the fourth power.six to the fourth power.
6 4Base
Exponent
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This exponent is read This exponent is read three to the 2three to the 2ndnd power or power or three squared.three squared.
3 2Base
Exponent
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Read These Exponents
77 to the 2nd poweror 7 squared
2
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Read These Exponents
1010 to the 3rd poweror 10 cubed
3
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What is the Exponent?
2 • 2 • 2 = 23
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What is the Exponent?
a • a • a • a = a4
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What is the Exponent?
(bc)(bc)(bc) = (bc)3
NOTICE that you keep the parenthesis around the variables (bc) because you
are cubing all the (bc)
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Write the Verbal PhasePower Verbal Phrase Means
27 “Seven to the 2nd power” 7 7“Seven squared”
35 “Five to the 3rd power” 5 5 5 “Five cubed”
49
125
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Write the Verbal PhasePower Verbal Phrase Meaning
49 “Nine to the 4th power” 9 9 9 9
52 “Two to the 5th power”2 2 2 2 2
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How to Multiply Out Exponents
= 3 • 3 • 3 • 33
927
81
4
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How to Multiply Out Exponents
= 2 • 2 • 2 • 2 • 22
48
16
5
32
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When simplifying exponents you must watch the sign and the parenthesis!
62
= 6•6 = 36
–62
= –6•6 = -36
(-6)2
=(-6)(-6) = 36
-(6)2
= - (6)(6)1 = -36
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An exponent is written in An exponent is written in exponential formexponential form when it is when it is simplified.simplified.
3322aa
33
Exponential Form
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An exponent is written in An exponent is written in factor formfactor form when it is written when it is written out. out.
3322aa
33= 3•3•a•a•a
Factor Form
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Factored Form Exponential Form
x • 8 • y • 8 • x 82x
2y
a • b • a • 2 2a2b
1
13 p p p r r 13p3r2
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Factored Form Exponential Form
5 • x • x • x 5x3
(5x)3 (5x)(5x)(5x) = 53x3
= 125x3
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Factored Form Exponential Form
8(ab)(ab) 8(ab)2
= 43x3w3y3(4xwy)3 (4xwy)(4xwy)(4xwy)
= 8a2b2
= 64x3w3y3
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Evaluate the expression if x = 3 and y = 4
2 2x +y2 23 +4
“Evaluate” mean to solve!
9 + 16
25
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Evaluate the expression if x = 3 and y = 4
22(x+y)22(3+4)
“Evaluate” mean to solve!
98
22(7)
2(49)
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Fractions With Exponents2
1
3
1 1
3 3
1
9
41
2
1 1 1 1
2 2 2 2
1
16
24
5
4 4
5 5
16
25
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Fractions With Exponents
22 3
2 23 3
49
21 5
1 15 5 1
25
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Fractions With Exponents
23 7
3 37 7
949
32 6
2 2 26 6 6
8216
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Take out your Study Guide (blue).
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An exponent tells how many times a number is multiplied by itself.
83Base
Exponent
#1
Factored Form
3 • 3 • a • a • a
Exponential Form
32a
3
x • y • x • 2 2x
2y
1
8•8•8 = 512
22 3
2 23 3 4
9
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# 2When simplifying exponents you must watch the sign and the parenthesis!
52
= 5•5 = 25
–52
= – (5)•(5) = –25
(-5)2
=(-5)(-5) = 25 –(5)2
= - (5)(5) = –251
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#3
1)
2)
3)
4)
25
42
310
212
5 5 25
2 2 2 2 16
10 10 10 1000
12 12 144
To find 54 on my calculator I type in 5 4^ = 625
5 yx 4 = 625
xy
x
5 4 = 625
5 4 = 625
Circle the method that works on your calculator!
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TEACHER NOTE: The lesson above was taught for Pre-Algebra &
Algebra.
The following slides were used for the class of Algebra Readiness
(lower level students) and slide #18-28 were taken out of the
lesson above since we were just introducing Exponents.
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Evaluate the Power“Evaluate” mean to solve!
1)
2)
3)
4)
25
42
310
212
5 5 25
2 2 2 2 16
10 10 10 1000
12 12 144
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7 units3
Addition:-One-Dimensional Growth
+ =+ 4 =
Multiplication: Two-Dimensional Growth
“Three added to four”
“Three times four” or “Three groups of four”
+ + =
+4 +4 4= 12 square units3(4)=
Multiplication is Repeated Addition
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Exponents: Three-Dimensional Growth
“Three to the third power”“Three to the fourth power”
3 33 33 3 3 3
327 un
43 3 3 3 3 381 un
Exponents is Repeated Multiplication
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Perimeter Area Volume 5
5
5
5
P = s+s+s+sP = 4s
P=4 5P=20 units
5
5
2A =s2A =5
A =25 2units
3V =s3V =5
V =125 3units
OneDimensional
TwoDimensional
ThreeDimensional
“Five Squared” “Five Cubed”
5 5
5
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I am going to give you a Study Guide (blue).Please take good notes on what we just learned! You can use these notes to help you with homework! You can use these notes on your test!
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Exponents & PowersAn exponent or power tells how manytimes a number is multiplied by itself.
34
BaseExponent
#1
25 “Five to the 2nd power” 5 5“Five squared”
37 “Seven to the 3rd power” 7 7 7 “Seven cubed”
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#2
1)
2)
3)
4)
25
42
310
212
5 5 25
2 2 2 2 16
10 10 10 1000
12 12 144
To find 54 on my calculator I type in 5 4^ = 625
5 yx 4 = 625
xy
x
5 4 = 625
5 4 = 625
Circle the method that works on your calculator!