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

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

4-2 Integer Exponents Warm Up Simplify. 1. 103 1000 2. 101 10 3. 104 10,000 4. 105 100,000 5. 106 1,000,000

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

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

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

4-6 Squares and Square Roots Warm Up Simplify. 1. 52 2. 82 25 64 3. 122 4. 152 144 225 5. 202 400

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. 1. 144 2. 256 ±12 ±16 3. 8 + 144 4. 7 289 20 119

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. 1. 119 10 and 11 2. 15 3 and 4 3. 2 1.4 4. 123 11.1

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