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3-1 Integer Exponents
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
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3-1 Integer Exponents
Warm UpEvaluate.
10001. 103
2. 101
3. 104
1
10,000
100,0004. 105
5. 106 1,000,000
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3-1 Integer Exponents
Problem of the Day
Find two different numbers for the values of x and y that will make xy and yx equal.2 and 4
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3-1 Integer Exponents
Learn to simplify expressions with negative exponents and to evaluate the zero exponent.
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3-1 Integer Exponents
Look for a pattern in the table to extend what you know about exponents to include negative exponents.
÷ 10 ÷ 10 ÷ 10 ÷ 10
102 101 100 10–1 10–2
10 • 10
100
10
10 1
1 110
110
= 0.1
110 • 10
1100
= 0.01
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3-1 Integer Exponents
Additional Example 1: Using a Pattern to Simplify Negative Exponents
Simplify. Write in decimal form.
A. 10–2
10–2 = 1
10 • 10
= 1100
= 0.01
B. 10–1
= = 0.1110
= 110
Extend the pattern from the table.
Multiply. Write as a decimal.
Extend the pattern from the table.
Multiply. Write as a decimal.
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3-1 Integer Exponents
Check It Out: Example 1A
10–8
=1
100,000,000
= 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
Extend the pattern from the table.
= 0.00000001
Multiply.
Write as a decimal.
Simplify. Write in decimal form.
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3-1 Integer Exponents
Check It Out: Example 1B
10–9
= 11,000,000,000
= 110 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
Extend the pattern from example 1A.
= 0.000000001
Multiply.
Write as a decimal.
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3-1 Integer Exponents
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3-1 Integer Exponents
5–3
Write the power under 1; change the sign of the exponent.
Additional Example 2A: Evaluating Negative Exponents
Simplify.
Find the product of three ’s.1 5
Simplify.
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3-1 Integer Exponents
(–10)–3 Write the power under 1; change the sign of the exponent.
Additional Example 2B: Evaluating Negative Exponents
Simplify.
Find the product of three ’s. 1 –10
Simplify.
1–10 • –10 • –10
–1000 1
= –0.001
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3-1 Integer Exponents
4–2
Write the reciprocal; change the sign of the exponent.
Check It Out: Example 2A
Simplify.
Find the product of two ’s.1 4
Simplify.
41 2
14 • 4
161
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3-1 Integer Exponents
(–7)–4
Write the reciprocal; change the sign of the exponent.
Check It Out: Example 2B
Simplfy.
Find the product of four ’s. 1 –7
Simplify.
1 –7
4
1
–7 • –7 • –7 • –7
2401 1
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3-1 Integer Exponents
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3-1 Integer Exponents
Subtract inside the parentheses.
Evaluate 5 – (6 – 4)–3 + (– 2)0.
Evaluate the exponents.
Additional Example 3: Using the Order of Operations
5 – (6 – 4)–3 + (–2)0
= 5 – (2)–3 + (–2)0
= 5 – + 1 1 8
= 5 7 8
Add and subtract from left to right.
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3-1 Integer Exponents
Subtract inside the parentheses.
Evaluate 3 + (7 – 4)–2 + (–8)0.
Evaluate the exponents.
Check It Out: Example 3
3 + (7 – 4)–2 + (–8)0
= 3 + (3)–2 + (–8)0
= 3 + + 1 1 9
= 4 1 9
Add.
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3-1 Integer Exponents
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
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3-1 Integer Exponents
Lesson Quiz
Evaluate the powers of 10.
1. 10–3 0.001
2. 10–7 0.0000001
Evaluate.
3. (–6)–2
4. 4 • 2–3 +10–1
5. 80 –(11 – 24)–2
1 36 3
524
25
6. (4w)–2 + w–1 for w = 4 65 256
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3-1 Integer Exponents
1. Evaluate 10–4.
A. –40
B. 0.001
C. 0.0001
D. 0.00001
Lesson Quiz for Student Response Systems
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3-1 Integer Exponents
2. Evaluate 2–4.
A. –8
B. 8
C. 16
D.
Lesson Quiz for Student Response Systems
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3-1 Integer Exponents
3. Evaluate 82 –(11 – 20)–2.
A. –8
B. 62
C. 64
D. 156
Lesson Quiz for Student Response Systems