Adding/Subtracting/Multiplying Exponents when bases are the same Absent Tues/Wed 11/13,14.

Slides:

Advertisements

Similar presentations

Basic Definitions a 3 a x a x a a as factor 3 times exponent power

Advertisements

Dividing Monomials.

Chapter R: Reference: Basic Algebraic Concepts

Lesson 6 Contents Example 1Multiply Powers Example 2Multiply Monomials Example 3Divide Powers Example 4Divide Powers Example 5Divide Powers to Solve a.

Evaluate this: 6-5x3÷5+1= Order of Operations Main Idea Evaluate expressions using the order of operations.

Imaginary & Complex Numbers

Objectives The student will be able to:

Objectives The student will be able to:

Multiply/Divide integers Absent 10/14

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.5 Dividing Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1.

Cubed Roots, Add/sub Sq. Roots and non-square integers notes Absent notes Tues/Wed 5/6,7.

Objectives The student will be able to:

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.4 Polynomials in Several Variables Copyright © 2013, 2009, 2006 Pearson Education, Inc.

Objective SWBAT simplify rational expressions, add, subtract, multiply, and divide rational expressions and solve rational equations.

Properties of Exponents

Zero exponent/Neg. exponent Absent Thurs/Fri 10/31-11/1

Use the substitution method

Bottoms Up Factoring. Start with the X-box 3-9 Product Sum

X-box Factoring. X- Box 3-9 Product Sum Factor the x-box way Example: Factor 3x 2 -13x (3)(-10)= x 2x 3x 2 x-5 3x +2.

Solve an equation by multiplying by a reciprocal

One step equations Add Subtract Multiply Divide Addition X + 5 = -9 X = X = X = X = X = 2.

Dividing Polynomials Monomials (Ex: 2x): It divides into everything…

Standard 10 add, subtract, multiply, and divide monomials and polynomials monomials are just one thing binomials are like bx + c polynomials are like ax².

Evaluating and Simplifying Algebraic Expressions

Simplify each polynomial Adding and Subtracting Polynomials.

 To add numbers in scientific notation: 1) Add the constants 2) Keep the exponent the same  Example: (2.1 x 10 5 ) + (3.2 x 10 5 ) = ( ) x 10.

8.1 Multiplying Monomials

Jeopardy MonomialsMultiplyingDividingNegative Exponents Applications Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy.

2.1 Sums and Differences of Polynomials

Objective 1: To multiply monomials. Objective 2: To divide monomials and simplify expressions with negative exponents.

Exponents Power base exponent means 3 factors of 5 or 5 x 5 x 5.

Do Now: Evaluate Multiplying Monomials Objectives SWBAT: 1) multiply monomials 2) Simplify expressions involving powers of monomials.

Solve the equation -3v = -21 Multiply or Divide? 1.

Monomials – Product and Quotient Remember your rules for multiplying and dividing variables…- When multiplying like variables, ADD your exponents When.

Essential Question: What is the first step for simplifying an exponential expression that contains negative exponents?

Adding and Subtracting Polynomials. 1. Determine the coefficient and degree of each monomial (Similar to p.329 #26)

Evaluating a Variable Expression To evaluate a variable expression:

Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

PROPERTIES OF EXPONENTS

Exponents Power base exponent means 3 factors of 5 or 5 x 5 x 5.

1-2 Order of Operations and Evaluating Expressions.

 Exponents MUST BE THE SAME before you can add/subtract 2 numbers written in scientific notation.  Example 1: 7.35 x 10 2 m x 10 2 m = ? › Are.

Algebra I Concept Test # 1 – Integers Practice Test − 15 A positive times a negative is ? = Simplify: (− 27) − 42 = 2.(6)(− 7) Negative 9 = 3.−

MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.

3.3 Day 1 Properties of logarithms –Use the product rule. –Use the quotient rule. –Use the power rule. –Expand logarithmic expressions. Pg. 407 # 2-36.

Powers and Laws of Exponents SWBAT write the standard form for numbers that are given in exponential form; write the exponential form for numbers that.

12.01 Multiplying Monomials. A monomial is a number, a variable, or a product of both. Examples: 8, x, 5y, x 3, 4x 2, – 6xy 7 Exponential Notation amam.

Adding and Subtracting Polynomials. 1. Determine whether the given expression is a monomial (Yes or No). For those that are monomials, state the coefficient.

LESSON 4-7 EXPONENTS & MULTIPLYING. When we multiply terms with exponents  ADD exponents of like variables.

Simplify MultiplyDivide Add & Subtract Proportion.

Dividing Monomials by Monomials. Think Back to September What is the exponent rule for dividing same bases? When dividing same bases subtract exponents.

Monomials Chapter 5.1. Vocabulary Monomial: an expression that is a number, a variable, or the product of a number and one or more variables. – Can not.

Dividing Monomials.

8 – Properties of Exponents No Calculator

Module 1 Day 3 Power Properties.

Multiply the following rational expressions. Show work!

Rules of Exponents Multiplying and powers

Goal: Simplify expressions with like terms

Rational Expressions – Simplifying

Section 8.1 Multiplication Properties of Exponents

Multiplying and Dividing Powers

Chapter 5-1 Exponents.

Multiplying and Factoring

Divide the number in C by 10.

Objectives Use properties to simplify logarithmic expressions.

The Laws of Exponents.

8.1 – 8.3 Review Exponents.

6.3 ADDING/SUBTRACTING POLYNOMIALS

Simplify: (3xy4)(-2x2y2) x3y6 xy2 -6x3y6

Presentation transcript:

Adding/Subtracting/Multiplying Exponents when bases are the same Absent Tues/Wed 11/13,14

To multiply powers with the same base, keep the base and add the exponents. x a x b = x a + b base base = base add exponents = = = = 8 4

Example 1 Simplify and write in exponential form (5) 3 (5) 4 (5) (5) 7 Solution What is exponential form? To re-write the answer with a base(factor) and exponent. What are the bases (factors) of this expression? (5) is the base (factor) of this expression. What are the exponents in this expression? The exponents are 3 & 4 When multiplying and bases are the same what do we do with exponents? We keep the base and add exponents. 5757

Example #2 Simplify (3x 2 y 3 )(4x 3 y 2 ) 3 4 x y x 5 y 5 Solution What are the coefficients of each monomial? The coefficients are 3 & 4 What do we do with the coefficients? We multiply the coefficients Are there any bases that are the same? Yes or no The x bases are the same and the y bases are the same. When multiplying and the bases are the same what do we do with the exponents? When bases are the same we add exponents. 12x 5 y 5

To divide powers with the same base, keep the base and subtract the exponents. Basex a = x a - b Basex b 4 5 = 4 5 – 2 = = 8 3 – 1 = 8 2 8

Example 3 Simplify the expression and write in exponential form: (-6) 10 (-6) 4 (-6) 10 – 4 (-6) 6 Solution What is exponential form? To re-write the answer with a base(factor) and exponent. What are the bases (factors) of this expression? The base (factor) is (-6) What are the exponents in this expression? The exponents of this expression are 10 & 4. When dividing and bases are the same what do we do with exponents? You keep the base and sub. exponents (-6) 6

Example 4 Simplify 30c 6 d 5 10c 4 d 3 30 c 6 – 4 d 5 – c 2 d 2 s olution What are the coefficients of each monomial? The coefficients are 30 & 10 What do we do with the coefficients? We divide the coefficients Are there any bases that are the same? Yes or no Both the C & D bases are the same. When dividing and the bases are the same what do we do with the exponents? When dividing and the bases are the same then you sub. The exponents 3c 2 d 2

To multiply a power to a power, keep the base and multiply the exponents. (x a ) b = x (a)(b) Base exponents (4 5 ) 2 = 4 5(2) = 4 10

Example 5 Simplify and write in exponential form: (-3 5 ) -2 (-3) (5)(-2) (-3) -10 Solution What is exponential form? To re-write the answer with a base(factor) and exponent. What is the base (factor) of this expression? The base (factor) is (-3) What are the exponents in this expression? The exponents are 5 & -2 When multiplying two powers (exponents) too the same base what do you do with exponents? You keep the base and multiply the exponents (-3) -10

Example 6 Simplify (3x 2 y 4 ) x 2(3) y 4(3) x 6 y 12 9x 6 y 4 Solution What are the factors in this monomial? The factors are 3, x 2, y 4 What do we do first? Draw your arrows What do we do with the exponents? A power(power) you multiply the exponents. Do we re-write this problem? Yes or no We re-write the problem with all the factors multiplied to the 3 rd power. 27x 6 y 12