1. Warm Ups Preview 4-1 Exponents 4-2 Integer Exponents
4-3 Properties of Exponents
4-4 Multiplying and Dividing Polynomials
4-5 Scientific Notation
4-6 Squares and Square Roots
4-7 Estimating Square Roots
4-8 The Real Numbers
4-9 The Pythagorean Theorem

2. Warm Up Find the product. 1. 5 • 5 • 5 • 5 625 2. 3 • 3 • 3 27
4-1 Exponents
Warm Up
Find the product.
1. 5 • 5 • 5 • 5
625
2. 3 • 3 • 3 27
3. (–7) • (–7) • (–7)
–343
4. 9 • 9 81

3. 4-2 Integer Exponents
Warm Up
Simplify.
1000 10
10,000 4.
105
100,000 5.
106
1,000,000

4. Warm Up Evaluate. 1. 33 27 2. 4 • 4 • 4 • 4 256 3. b2 for b = 4 16
4-3 Properties of Exponents
Warm Up
Evaluate.
1. 33 27
2. 4 • 4 • 4 • 4
256
3. b2 for b = 4 16
4. n2r for n = 3 and r = 2 18

5. Write in exponential form. 1. 6 · 6 · 6 · 6 · 6 2. 3x · 3x · 3x · 3x
4-4 Multiplying and Dividing Monomials
Warm Up
Write in exponential form.
1. 6 · 6 · 6 · 6 · 6
2. 3x · 3x · 3x · 3x
Simplify.
3. 34
4. (–3)5
5. (24)5
6. (42)0 65
(3x)4 81
–243
220 1

6. 4-5 Scientific Notation
Warm Up
Order each set of numbers from least to greatest.
, 10 , 10 , 10 4 –2 –1
10 , 10 , 10 , 10 4 –1 –2
2. 8 , 8 , 8 , 8 2 –2 3
8 , 8 , 8 , 8 3 2 –2
3. 2 , 2 , 2 , 2 3 –6 –4 1
2 , 2 , 2 , 2 3 1 –4 –6
, 5.2 , 5.2 , 5.2 2 9 –1 –2
5.2 , 5.2 , 5.2 , 5.2 9 2 –1 –2

7. 4-6 Squares and Square Roots
Warm Up
Simplify. 25 64
144
225
5. 202
400

8. Find the two square roots of each number.
4-7 Estimating Square Roots
Warm Up
Find the two square roots of each number.
Evaluate each expression.
±12
±16 20
119

9. Warm Up 4-8 The Real Numbers
Each square root is between two integers. Name the two integers.
Use a calculator to find each value Round to the nearest tenth.
10 and 11
3 and 4
1.4
11.1

10. Estimate each square root to nearest hundredth.
4-9 The Pythagorean Theorem
Warm Up
Estimate each square root to nearest hundredth.
1. √30
2. √14
3. √55
4. √48
5.48
3.74
7.42
6.93