8.2 Exponenrts
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This document provides a summary of key concepts from an algebra warm up on exponents including: when multiplying like bases you add exponents, when multiplying monomials you multiply coefficients and add exponents of like bases, when raising a power to a power you multiply the exponents, an exponent applied outside parentheses applies to everything inside, and that when raising a negative number to an exponent, an even exponent gives a positive answer while an odd exponent gives a negative answer. It directs the reader to specific pages to review these exponent rules and examples.
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The document discusses various rules and concepts related to exponents and radicals. It presents examples showing how to simplify expressions using rules such as adding exponents with the same base, distributing exponents, setting exponents of zero equal to one, subtracting exponents with the same base, changing negative exponents to positive forms, and properties of radicals like adding only if they have the same radicand. It emphasizes working through examples as the most important way to understand and apply the rules.
Exponents Rules
This document provides rules and explanations for operations involving exponents. It discusses:
1) The rule for adding or subtracting exponents with the same base, such as am + n = amxn or am ÷ an = am-n.
2) Exceptions when the bases are different, such as 23 x m4 ≠ 2m7.
3) The power of a power rule, such as (n2)4 = n8, which only works for a single positive base in brackets.
4) How to expand products and quotients with the same exponents, such as (2a)2 = 4a2, and simplify fractions with different bases but the same exponents.
Exponents Rules
This document provides rules and examples for operations involving exponents. It explains that when bases are the same, exponents can be added or subtracted. It also discusses the power of a power rule where the outer exponent is multiplied by the inner one. There are warnings that these rules only apply when bases are the same or there is a single base inside brackets. Negative exponents are explained as reciprocals with the base moving above or below the fraction line.
Division of numbers in exponential form
This document covers properties of exponents, including reviewing the multiplication property and introducing the division property. It provides examples of simplifying expressions using exponents by adding exponents when multiplying terms with the same base or subtracting exponents when dividing terms with the same base. It also has reminders about the goal and agenda for the lesson which is applying exponent properties to generate equivalent numerical expressions.
January 29 30
The document provides practice problems on simplifying monomial expressions and dividing monomials. It begins with examples of dividing monomials using the property that when dividing powers with the same base, you subtract the exponents. It then provides practice problems for students to divide monomial expressions and simplify expressions using exponent properties. Sample problems are worked through step-by-step as examples.
Module 1 topic 1 notes
This document provides an overview of solving linear equations, including:
- Slides cover solving linear equations and practice questions
- Includes an algebra cheat sheet and guide for using a graphing calculator
- Defines a linear equation and provides examples of solving linear equations algebraically by isolating the variable
- Shows checking solutions by plugging them back into the original equation
- Provides word problems applying linear equations to real-world scenarios like temperature conversion and asset depreciation
Operaciones Multiplicativas
This document discusses properties of exponents and operations with polynomials. It explains that to multiply or divide powers with the same base, you add or subtract their exponents. Some examples are provided of multiplying and dividing terms with exponents. The document then discusses multiplying monomials by applying exponent properties, multiplying a monomial by a polynomial using distributive properties, and multiplying two polynomials by multiplying terms.
Multiplying Polynomials I
This document reviews rules of exponents and introduces multiplying polynomials using the distributive property and box method. It defines monomials, binomials, and trinomials. Examples are provided of distributing a monomial over a binomial using the box method, including rewriting the expression by combining like terms.
Exponents and powers by arjun rastogi
EXPONENTS AND POWERS MUST SEEEEEEEEEEEEEE
IF YOU WANT ME TO MAKE YOUR OWN SUBJECT PPT CALL ME ON NUMBER
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E2
This document provides an overview of exponent rules, including:
- When multiplying or dividing terms with the same base, you add or subtract their exponents respectively
- When raising a power to another power, you multiply the exponents
- A product or quotient raised to a power means each term is raised to that power
- A number raised to the zero power is equal to 1, except for 0 raised to zero which is undefined
- A negative exponent flips the term with that exponent to the denominator
Several examples are given to demonstrate each rule and mixed practice problems are provided for application.
Simple Equations I
This document discusses solving one-step linear equations using addition and subtraction. It defines key terms like equations, solutions, and isolating variables. It explains that when transforming equations, the same operations must be applied to both sides to maintain equivalence. Inverse operations like addition and subtraction can isolate variables. Examples show how to isolate variables using addition or subtraction and solve equations. Students are then prompted to solve practice equations on their own. The document also discusses using equations to solve real-world problems, like finding a person's maximum heart rate based on their age.
Rules of exponents 1
The document discusses exponent rules for multiplying, dividing, raising powers, and applying exponents to products and quotients. It provides examples and practice problems for each rule. The key rules are: when multiplying terms with the same base, add the exponents; when dividing terms with the same base, subtract the exponents; when raising a power to another power, multiply the exponents; and when applying an exponent to a product or quotient, raise each term in the product or quotient to that exponent.
Module 9.4.9.5,9.6
This document discusses solving radical equations through multiple steps:
1) Isolate the radical on one side of the equation and square both sides to eliminate the radical.
2) Radicals can also be cubed roots, requiring the same process of isolating the radical and squaring both sides.
3) Radical equations can also be solved by graphing each side as functions and finding the intersection point of the graphs.
4) Transformations of radical equations, such as changing coefficients, affect the graph by shifting it up or down (changing k) or left or right (changing h).
Laws-of-Exponents by our teacher which name is in the PowerPoint
This document provides an overview of laws of exponents and how they are applied to simplify expressions involving exponents. It outlines five key laws:
1. The product rule states that when multiplying expressions with the same base, add the exponents.
2. The power of a product rule distributes exponents to each term when a product is raised to a power.
3. The quotient rule subtracts exponents when dividing expressions with the same base.
4. The power of a quotient rule distributes exponents to both the numerator and denominator.
5. The power of a power rule simply multiplies the exponents when a power is raised to another power.
Worked examples are provided to demonstrate how to apply
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Laws-of-Exponents by our teacher which name is in the PowerPoint
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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8.2 Exponenrts
- 1. Algebra Warm Up: pg. 382 # 68-69 REMEMBER --becasue of the ABS value-- split into 2 cases to solve!
- 2. 8.2 Laws of Exponents: Powers and Products pg. 377 -382 So yesterday you learned: When multiplying like bases--you add exponents When multiplying monomials--you multiply the coefficents, add the exponents of the like bases
- 3. The second rule of exponents: (3 parts) Raising power to a power. In this case you will be applying an exponent to a set of parentheses (multiplying the exponents together)
- 4. pg. 378
- 5. Raising Monomials to a Power In this case--again you are applying the exponent outside the ( ) to everything inside! JUST like you use Distributive Property--The exponent applies to EVERY part inside the ( )--THEN simplify if you can!
- 6. pg. 379
- 7. pg. 379
- 8. pg. 380
- 9. Sometimes you will have word problems--This just involves SUBSTITUTING an expression into a formula
- 10. Powers of -1 Recall from chapter 2- negative x megative = positive negative x positive = negative positive x negative = negative positive x positive = posistive This idea applies to exponents and negative numbers! EVEN exponent applied to negative bases GIVES positive answer (negatives cancel out) ODD exponent applied to negative bases GIVES negative answer
- 11. pg. 380
- 12. Now you try them together! pg. 381 # 2-25 DON'T forget about the rule from yesteday--They will still apply!