Lesson 8.3 Define and Use Zero and Negative Exponents After today’s lesson, you should be able to...
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Lesson 8.3 Define and Use Zero and Negative Exponents After today’s lesson, you should be able to use zero and negative to simplify expressions. (CA 2.0)
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Transcript of Lesson 8.3 Define and Use Zero and Negative Exponents After today’s lesson, you should be able to...
Lesson 8.3 Define and Use Zero and Negative Exponents
After today’s lesson, you should be able to use zero and negative to
simplify expressions. (CA 2.0)
Power Value 1
1
1
1
1
1
1
1
Zero Exponent
Ex 1) Simplify Method 1: Use Expanded Form
Zero Exponent
Method 2: Use the Quotient of Powers Rule
Definition: Zero exponent
Words: a to the zero power is 1.
Algebra:
Examples: Simplify.
2)
Examples: Simplify.
3)
Examples: Simplify.
4) You Try:
Power Value
Negative Exponents
Using Patterns to Discover the Meaning Behind Negative Exponents
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000
10,000
1000
100
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
10,000
1000
100
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000
1000
100
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙
1000
100
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000
100
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙
100
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1
Complete the following table. Use only a base of 10.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
1100
11000
110,000
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110
1100
11000
110,000
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
11000
110,000
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙
11000
110,000
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙ 10-2
11000
110,000
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙ 10-2
11000
110 10 10∙ ∙
110,000
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙ 10-2
11000
110 10 10∙ ∙ 10-3
110,000
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙ 10-2
11000
110 10 10∙ ∙ 10-3
110,000
110 10 10 10∙ ∙ ∙
Now let’s continue the pattern.Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙ 10-2
11000
110 10 10∙ ∙ 10-3
110,000
110 10 10 10∙ ∙ ∙ 10-4
What should you learn from this?Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙ 10-2
11000
110 10 10∙ ∙ 10-3
110,000
110 10 10 10∙ ∙ ∙ 10-4
What should you learn from this?Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙ 10-2
11000
110 10 10∙ ∙ 10-3
110,000
110 10 10 10∙ ∙ ∙ 10-4
1) Any number raised to the zero power is always 1.
What should you learn from this?Stand. Form Expanded Form Expon. Form
100,000 10 10 10 10 1∙ ∙ ∙ ∙0
105
10,000 10 10 10 10∙ ∙ ∙ 104
1000 10 10 10∙ ∙ 103
100 10 10∙ 102
10 10 101
1 100
110
110 10-1
1100
110 10∙ 10-2
11000
110 10 10∙ ∙ 10-3
110,000
110 10 10 10∙ ∙ ∙ 10-4
1) Any number raised to the zero power is always 1.
2) A negative exponent will create a fraction.
A negative exponent will result in the reciprocal of the base with a positive exponent.
A negative exponent will result in the reciprocal of the base with a positive exponent.
5-2 =
A negative exponent will result in the reciprocal of the base with a positive exponent.
5-2 = 15( )
2
A negative exponent will result in the reciprocal of the base with a positive exponent.
5-2 = 15( )
2
= 15∙
15
= 125
A negative exponent will result in the reciprocal of the base with a positive exponent.
4-3 =
A negative exponent will result in the reciprocal of the base with a positive exponent.
4-3 = 14( )
3
A negative exponent will result in the reciprocal of the base with a positive exponent.
4-3 = 14( )
3
= 14∙
14
= 164∙1
4
A negative exponent will result in the reciprocal of the base with a positive exponent.
3-4 =
A negative exponent will result in the reciprocal of the base with a positive exponent.
3-4 = 13( )
4
A negative exponent will result in the reciprocal of the base with a positive exponent.
3-4 = 13( )
4
= 13∙
13
= 181∙1
3 ∙13
A negative exponent will result in the reciprocal of the base with a positive exponent.
(-6)-3 =
( )
A negative exponent will result in the reciprocal of the base with a positive exponent.
= 1-6
3
(-6)-3
( )
A negative exponent will result in the reciprocal of the base with a positive exponent.
= 1-6
3
= 1-6∙
1-6
= 1216∙1
-6-(-6)-3
Practice Time
Evaluate.
1) 2-3 = 2) 4-4 =
3) (-2)-4 = 4) (-5)-3 =
5) 80 = 6) (-4)0 =
Evaluate.
1) 2-3 = 2) 4-4 =
3) (-2)-4 = 4) (-5)-3 =
5) 80 = 6) (-4)0 =
18
Evaluate.
1) 2-3 = 2) 4-4 =
3) (-2)-4 = 4) (-5)-3 =
5) 80 = 6) (-4)0 =
18
1256
Evaluate.
1) 2-3 = 2) 4-4 =
3) (-2)-4 = 4) (-5)-3 =
5) 80 = 6) (-4)0 =
18
1256
116
Evaluate.
1) 2-3 = 2) 4-4 =
3) (-2)-4 = 4) (-5)-3 =
5) 80 = 6) (-4)0 =
18
1256
116
1125-
Evaluate.
1) 2-3 = 2) 4-4 =
3) (-2)-4 = 4) (-5)-3 =
5) 80 = 6) (-4)0 =
18
1256
116
1125-
1
Evaluate.
1) 2-3 = 2) 4-4 =
3) (-2)-4 = 4) (-5)-3 =
5) 80 = 6) (-4)0 =
18
1256
116
1125-
1 1
Evaluate. Remember the order of operations.
1) 4-2 + 2-3 =
2) 50 – (6)-2 =
3) 4(3 + 5)0 + 42 =
4) (3 + 5)-2 =
Evaluate. Remember the order of operations.
1) 4-2 + 2-3 =
2) 50 – (6)-2 =
3) 4(3 + 5)0 + 42 =
4) (3 + 5)-2 =
316
Evaluate. Remember the order of operations.
1) 4-2 + 2-3 =
2) 50 – (6)-2 =
3) 4(3 + 5)0 + 42 =
4) (3 + 5)-2 =
316
3536
Evaluate. Remember the order of operations.
1) 4-2 + 2-3 =
2) 50 – (6)-2 =
3) 4(3 + 5)0 + 42 = 20
4) (3 + 5)-2 =
316
3536
Evaluate. Remember the order of operations.
1) 4-2 + 2-3 =
2) 50 – (6)-2 =
3) 4(3 + 5)0 + 42 = 20
4) (3 + 5)-2 =
316
164
3536
Evaluate. Remember the order of operations.
5) 2-1 + (-2)-2 =
6) 52 – 30 =
7) 2(1 + 3)-2 =
8) (6 + 3)2 + (6 + 3)-2 =
Evaluate. Remember the order of operations.
5) 2-1 + (-2)-2 =
6) 52 – 30 =
7) 2(1 + 3)-2 =
8) (6 + 3)2 + (6 + 3)-2 =
34
Evaluate. Remember the order of operations.
5) 2-1 + (-2)-2 =
6) 52 – 30 =
7) 2(1 + 3)-2 =
8) (6 + 3)2 + (6 + 3)-2 =
34
24
Evaluate. Remember the order of operations.
5) 2-1 + (-2)-2 =
6) 52 – 30 =
7) 2(1 + 3)-2 =
8) (6 + 3)2 + (6 + 3)-2 =
34
24
18
Evaluate. Remember the order of operations.
5) 2-1 + (-2)-2 =
6) 52 – 30 =
7) 2(1 + 3)-2 =
8) (6 + 3)2 + (6 + 3)-2 = 81
34
24
18
181
Definition: Negative exponent
Words:
Algebra:
Examples: Evaluate the expression.
5)
Examples: Evaluate the expression.
6)
Examples: Evaluate the expression.
7)
=49
Examples: Evaluate the expression.
8) You Try
Examples: Evaluate the expression.
9)
Examples: Evaluate the expression.
10)
Examples: Evaluate the expression.11) You Try
Examples: Evaluate the expression.12) You Try
Examples: Simplify the expression. Write your answer using only positive exponents.
13)
Examples: Simplify the expression. Write your answer using only positive exponents.
14)
Examples: Simplify the expression. Write your answer using only positive exponents.
15)
Examples: Simplify the expression. Write your answer using only positive exponents.
16) You Try
Examples: Simplify the expression. Write your answer using only positive exponents.
17)
Examples: Simplify the expression. Write your answer using only positive exponents.
18)
Examples: Simplify the expression. Write your answer using only positive exponents.
19) You Try
