(8) Lesson 1.2 - Powers and Exponents
- 1. Course 3, Lesson 1-2 Write each fraction or mixed number as a decimal. 1. 2. 3. Write each decimal as a fraction or mixed number in simplest form. 4. 0.08 5. 1.375 6. The largest moth is the Atlas moth. The Atlas moth is 11.8 inches long. What is the length of an Atlas moth written as a mixed number? 7 8 5 12 3 2 20
- 2. Course3, Lesson 1-2 ANSWERS 1. 0.875 2. 3. 2.15 4. 5. 6. 0.416 2 25 3 1 8 4 11 in. 5
- 3. WHY is it helpful to write numbers in different ways? The Number System Course3, Lesson 1-2
- 4. Course3, Lesson 1-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. The Number System • 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning.
- 5. • To write and evaluate expressions using exponents Course3, Lesson 1-2 The Number System
- 6. • power • base • exponent Course3, Lesson 1-2 The Number System
- 7. 1 Need Another Example? 2 Step-by-Step Example 1. Write the expression using exponents. (–2) • (–2) • (–2) • 3 • 3 • 3 • 3 The base –2 is a factor 3 times, and the base 3 is a factor 4 times. (–2) • (–2) • (–2) • 3 • 3 • 3 • 3 = (–2)3 • 34
- 8. Answer Need Another Example? Write (–9) • (–9) • (–9) • (–9) • (–9) • 4 • 4 • 4 as an expression using exponents. (–9)5 • 43
- 9. 1 Need Another Example? 2 3 Step-by-Step Example 2. Write the expression using exponents. a • b • b • a • b Use the properties of operations to rewrite and group like bases together. The base a is a factor 2 times, and the base b is a factor 3 times. a • b • b • a • b = a • a • b • b • b = a2 • b3
- 10. Answer Need Another Example? Write x • y • x • y • x • x as an expression using exponents. x4 • y2
- 11. 1 Need Another Example? 2 Step-by-Step Example 3. Evaluate . = Write the power as a product. Multiply
- 13. 1 Need Another Example? 2 3 4 Step-by-Step Example 4. The deck of a skateboard has an area of about 25 • 7 square inches. What is the area of the skateboard deck? 25 • 7 = 2 • 2 • 2 • 2 • 2 • 7 Write the power as a product. Associative Property= (2 • 2 • 2 • 2 • 2) • 7 = 32 • 7 or 224 The area of the skateboard deck is about 224 square inches. Multiply.
- 14. Answer Need Another Example? A racquetball court has an area of 2 • 42 • 52 square feet. What is the area of the racquetball court? 800 ft2
- 15. 1 Need Another Example? 2 3 Step-by-Step Example 5. Evaluate the expression if a = 3 and b = 5. a2 + b4 a2 + b4 = 32 + 54 Replace a with 3 and b with 5. Write the powers as products.= (3 • 3) + (5 • 5 • 5 • 5) = 9 + 625 or 634 Add.
- 16. Answer Need Another Example? Evaluate x3 + y5 if x = 4 and y = 2. 96
- 17. 1 Need Another Example? 2 3 Step-by-Step Example 6. Evaluate the expression if a = 3 and b = 5. (a – b)2 (a – b)2 = (3 – 5)2 Replace a with 3 and b with 5. Perform operations in the parentheses first. = (–2)2 = (–2) • (–2) or 4 Write the powers as products. Then simplify.
- 18. Answer Need Another Example? Evaluate (x + y)2 if x = 4 and y = 2. 36
- 19. How did what you learned today help you answer the WHY is it helpful to write numbers in different ways? Course 3, Lesson 1-2 The Number System
- 20. How did what you learned today help you answer the WHY is it helpful to write numbers in different ways? Course 3, Lesson 1-2 The Number System Sample answers: • Writing numbers using powers is a short way of writing very large numbers. • You would use exponents when you work with the metric system since the metric system is based on powers of ten.
- 21. Write about how you think powers and exponents connect with multiplying and dividing monomials. Ratios and Proportional RelationshipsThe Number System Course 3, Lesson 1-2