Chapter4.2
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This document provides examples and explanations for evaluating expressions with negative exponents by changing the sign of the exponent and writing the expression under 1. It demonstrates simplifying expressions like 10-2 = 0.01 by multiplying factors of 10, and shows that subtracting 1 from the exponent decreases the value by a factor of 10. The order of operations and evaluating nested expressions with exponents is also addressed.
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Exponent1
1. Exponents indicate how many times a base is multiplied by itself. The laws of exponents describe how to manipulate exponents in algebraic expressions.
2. When multiplying or dividing expressions with the same base, exponents are added or subtracted. When raising a power to another exponent, the exponents are multiplied.
3. Negative exponents indicate the reciprocal of the base with a positive exponent. An exponent of zero equals one.
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This document discusses the laws of exponents. It defines what exponents mean and provides examples. The key laws of exponents covered are:
1) Multiplying powers with the same base means adding the exponents
2) Dividing powers with the same base means subtracting the exponents
3) Raising a power to another exponent means multiplying the exponents
4) A number with a zero exponent equals one.
Worked examples applying each law are provided.
Donna g. bautista
The document discusses the eight laws of exponents:
1) Exponential form indicates how many times the base multiplies itself using exponents.
2) When multiplying powers with the same base, add the exponents.
3) When dividing powers with the same base, subtract the exponents.
4) When raising a power to an exponent, multiply the exponents.
7.4 notes1[1]
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Exponent1
1. Exponents indicate how many times a base is multiplied by itself. The laws of exponents describe how to manipulate exponents in algebraic expressions.
2. When multiplying or dividing expressions with the same base, exponents are added or subtracted. When raising a power to another exponent, the exponents are multiplied.
3. Negative exponents indicate the reciprocal of the base with a positive exponent. An exponent of zero equals one.
E1
This document discusses the laws of exponents. It defines what exponents mean and provides examples. The key laws of exponents covered are:
1) Multiplying powers with the same base means adding the exponents
2) Dividing powers with the same base means subtracting the exponents
3) Raising a power to another exponent means multiplying the exponents
4) A number with a zero exponent equals one.
Worked examples applying each law are provided.
Donna g. bautista
The document discusses the eight laws of exponents:
1) Exponential form indicates how many times the base multiplies itself using exponents.
2) When multiplying powers with the same base, add the exponents.
3) When dividing powers with the same base, subtract the exponents.
4) When raising a power to an exponent, multiply the exponents.
7.4 notes1[1]
Linear systems can be solved by multiplying one or both equations by a constant so that adding or subtracting the equations eliminates one variable. The document provides two examples of solving linear systems - one where one equation is multiplied and then added, and another where both equations are multiplied and then subtracted. It also provides practice problems for readers to try solving linear systems on their own.
Project 2 Revised
The Purdue Engineering Fountain serves multiple purposes beyond just being a water fountain. It acts as a colorful work of art at night and is a popular spot for students to walk between classes, relax, socialize, and take photos. The fountain is also part of Purdue's annual Fountain Run tradition. While its main function is as a water fountain, it provides students with an iconic gathering place on campus.
Quién es quién
Este documento lista los nombres de varias personas, incluyendo a Alin, Jesús, Rachel, Víctor, Fátima, entre otros. Fue realizado por el Departamento de Plástica del IES Montes de Cabañeros y agradece a todos los participantes, tanto alumnos como profesores, en enero de 2011 en Horcajo de los Montes.
Poch dela rosa_how to use pod-o-matic.ppt
To use Pod-o-Matic, create a free account by filling out information on their website. Then browse podcasts by category or location and listen by downloading files. You can also publish your own podcasts or minicasts by following creation steps in the site menus.
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This document provides instructions and materials for a math lesson on similarity and scale factors. It includes examples of similar figures with questions about their side lengths, scale factors, and areas. It also discusses how police use measurements and similar figures to determine characteristics like a criminal's height from surveillance photos. Students are asked to use a photo of a teacher holding an object of known size to calculate the teacher's height, and to explain how police may have used a similar technique to determine a robber's height from a store surveillance photo.
9.9
The document provides examples of factoring polynomials completely. It begins by outlining guidelines for factoring polynomials completely, such as factoring out the greatest common monomial factor, looking for differences of squares or perfect square trinomials, and factoring trinomials and polynomials with four terms by grouping. It then works through examples of factoring various polynomials completely by applying these guidelines. These include factoring trinomials, solving a polynomial equation, and solving a multi-step problem involving factoring a polynomial to find dimensions.
9.8
The document discusses factoring polynomials using the difference of squares pattern and perfect square trinomial pattern. It provides examples of factoring expressions involving these patterns, including solving polynomial equations. The examples illustrate factoring expressions with variables and evaluating expressions to solve vertical motion problems.
9.5
The document provides examples and explanations of the zero-product property, factoring polynomials, finding roots of polynomials, and solving equations involving vertical motion. It demonstrates using the zero-product property to solve equations by setting each factor equal to 0. It explains how to factor polynomials by finding the greatest common monomial factor. And it shows how to model and solve word problems involving the vertical motion of projectiles.
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Chapter4.2
- 1. Warm Up California Standards Lesson Presentation Preview
- 2. Warm Up Simplify. 1000 1. 10 3 2. 10 1 3. 10 4 10 10,000 100,000 4. 5. 1,000,000 10 5 10 6
- 3. NS2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base. AF2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents. California Standards
- 4. Look at the pattern shown in the table to extend what you know about exponents to include negative exponents. ÷ 10 ÷ 10 ÷ 10 ÷ 10 10 2 10 1 10 0 10 – 1 10 – 2 10 • 10 100 10 10 1 1 1 10 1 10 = 0.1 1 10 • 10 1 100 = 0.01
- 5. Notice from the chart that as the exponents decrease by 1, the value of the expression decreases by a factor of 10. ÷ 10 ÷ 10 ÷ 10 ÷ 10 10 2 10 1 10 0 10 – 1 10 – 2 10 • 10 100 10 10 1 1 1 10 1 10 = 0.1 1 10 • 10 1 100 = 0.01
- 6. Additional Example 1: Using a Pattern to Evaluate Negative Exponents Simplify the powers of 10. A. 10 –2 B. 10 –1 Multiply. Write as a decimal. Multiply. Write as a decimal. 10 –2 = 1 10 • 10 = 1 100 = 0.01 = = 0.1 1 10 10 = – 1 1 10
- 7. Check It Out! Example 1A Simplify the powers of 10. 10 –8 Extend the pattern from the table. = 0.00000001 Multiply. Write as a decimal. = 1 100,000,000 10 –8 = 1 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
- 8. Check It Out! Example 1B 10 –9 Extend the pattern from Example 1A. = 0.000000001 Multiply. Write as a decimal. Simplify the powers of 10. = 1 1,000,000,000 10 –9 = 1 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
- 10. 5 –3 Write the power under 1; change the sign of the exponent. Additional Example 2A: Evaluating Negative Exponents Simplify. Simplify. Find the product. 1 5 • 5 • 5 = 125 1 =
- 11. (–10) –3 Write the power under 1; change the sign of the exponent. Additional Example 2B: Evaluating Negative Exponents Simplify. Simplify. = –0.001 Find the product. 1 – 10 • –10 • –10 = – 1000 1 =
- 12. 4 –2 Write the power under 1; change the sign of the exponent. Check It Out! Example 2A Simplify. Simplify. Find the product. 1 4 • 4 = 16 1 =
- 13. (–7) –4 Write the power under 1; change the sign of the exponent. Check It Out! Example 2B Simplify. Simplify. Find the product. 1 – 7 • –7 • –7 • –7 = 2401 1 =
- 15. Subtract inside the parentheses. Simplify 5 – (6 – 4) –3 + (–2) 0 . Rewrite 2 -3 . Additional Example 3: Using the Order of Operations 5 – (6 – 4) –3 + (–2) 0 5 – (2) –3 + (–2) 0 Add and subtract from left to right. Simplify the powers. 5 7 8 5 – + 1 1 2 3 5 – + 1 1 8
- 16. Subtract inside the parentheses. Simplify 3 + (7 – 4) –2 + (–8) 0 . Rewrite 3 -2 . Check It Out! Example 3 3 + (7 – 4) –2 + (–8) 0 3 + (3) –2 + (–8) 0 Simplify the powers. Add. 4 1 9 3 + + 1 1 9 3 + + (–8) 0 1 3 2
- 17. Lesson Quiz Simplify the powers of 10. 1. 10 –3 0.001 2. 10 –7 0.0000001 Simplify. 3. (–6) –2 4. 4 • 2 –3 + 10 –1 5. 8 0 – (11 – 2 4 ) –2 1 36 3 5 24 25 6. Evaluate (4 w ) –2 + w –1 for w = 4. 65 256