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Factored FormExponential Form x 8 y 8 x 8 2 x 2 y a b a 2 2a 2 b 1 13 p p p r r 13p 3 r 2
copyright©amberpasillas2010 n n n n x 3 x x x = exponent Base When The Bases Are The Same x a = x b x a + b n 3 = n 2 n 3 + 2 Ex: = = n 5 n 5 ADD EXPONENTS!
copyright©amberpasillas2010 1) 2) 3) 4) 5) 6) HINT: Multiply coefficients
copyright©amberpasillas2010 ( ) Power to Power Rule x a = b x ab n 3 2 (n n n) Ex: 2 = = n 6 = n 3 2 = n 6 When You Have an Exponent On The Outside of Parenthesis MULTIPLY EXPONENTS!
copyright©amberpasillas2010 1) 2) 3)4)
copyright©amberpasillas2010 Prime Numbers- A Prime number is a whole number with only 2 factors, one and itself. Composite Numbers- A Composite number is a number that has more than two factors. Example: 2, 3, 5, 7, 11, 13, 17… Example: 4, 6, 8, 9, 10, 12, 14, 15…
copyright©amberpasillas2010 Composite Number - Composite numbers can be written as the product of prime numbers. This is called: Prime Factorization - Prime Factorization is the unique set of prime numbers whose product equals a given number.
Prime Factorization is when you write a number as the product of prime numbers. Factor Tree 36 2 18 2 9 3 3 Circle the prime numbers
copyright©amberpasillas2010 Write the prime factorization of the number 24. 24 2 12 2 6 4 6 2 3 2 2 2 3 Circle the prime numbers Notice you get the same answer doing it two different ways! No matter how your start, you will get the same answer! That is why prime factorization is so unique!
copyright©amberpasillas2010 96 2 48 6 8 2 3 2 4 2 2 Notice we put them in order from least to greatest
copyright©amberpasillas2010 240 2 120 2 60 2 30 2 15 3 5
copyright©amberpasillas2010 9ab 9 ab a b 3 3
copyright©amberpasillas2010 6 m m 2 3
== Write each expression in FACTOR FORM t hen simplify.
== Write each expression in FACTOR FORM then simplify.
copyright©amberpasillas2010 == Write each expression in FACTOR FORM then simplify.
copyright©amberpasillas2010 12 18 2 3 ÷ 6 6 = Simplify or Reduce this fraction.
copyright©amberpasillas2010 12 20 3 5 ÷ 4 4 = Simplify or Reduce this fraction.
copyright©amberpasillas2010 9 21 3 7 ÷ 3 3 = Simplify or Reduce this fraction.
Take Out Your Study Guide!!! copyright©amberpasillas2010
#13 = x 8+5 x 8 x 5 (4a 7 b) 3 = 4 3 a 7 3 b 3 = x 13 = 64 a 21 b 3 Product of a Power Property Power of a Power Property = (-12) 2 (-3 4) 2 =144 Power of a Product Property = (-12)(-12)
copyright©amberpasillas2010 Prime Factorization is when you write a number as the product of prime numbers. Factor Tree 36 #14 2 18 2 9 3 3 Circle the prime numbers
copyright©amberpasillas2010 Factoring #15 1) == 2) == 12 2 6 2 3
Copyright©amberpasillas2010. Prime Numbers- A Prime number is a whole number with only 2 factors, one and itself. Composite Numbers- A Composite number.
Copyright©amberpasillas2010. Exponents give us many shortcuts for multiplying and dividing quickly. Each of the key rules for exponents has an importance.
Copyright©amberpasillas2010. Simplify two different ways. == = =
Two Important Math Properties to Know Commutative Property of Multiplication: The order of a Mulitplication Problem doesn’t matter, the product is still.
Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being raised to the exponent. Ex is the base.
Copyright©amberpasillas2010. A mixed number number has a part that is a whole number and a part that is a fraction. = copyright©amberpasillas2010.
EXAMPLE 2 Identifying Prime and Composite Numbers Write all the factors of the number and tell whether it is prime or composite. a. 32 e. 149 b. 39 c.
Copyright©amberpasillas2010 An exponent tells how many times a number is multiplied by itself. 8 3 Base Exponent #1 Factored Form 3 3 a a a Exponential.
Copyright©amberpasillas2010. Factor - A whole number or variable expression that divides evenly into a given whole number or variable expression. List.
Factors, Primes & Composite Numbers 6 th grade math.
Factors, Primes & Composite Numbers Chapter 4.1. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product.
Preparation for NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g.
Copyright©amberpasillas2010 RULES FOR DIVISIBILITY #1 A Number Is Divisible By: IF The last digit is even (0, 2, 4, 6, 8) The last 2 digits.
Factors, Primes & Composite Numbers. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product.
Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.
Factors, Primes & Composite Numbers by Ms. Green.
7.1 Factors and Greatest Common Factors (GCF) CORD Math Mrs. Spitz Fall 2006.
N UMBER T HEORY AND F RACTIONS R EVIEW. N UMBER T HEORY Prime Number- A whole number that can only be divided by 1 and itself Ex. 2,3,5,7,11,13… Composite.
Homework Answers (1-2 Worksheet). Combining Like Terms Term: Part of the expression or equation separated by + and - Variable: Letter that represents.
Factors, Primes & Composite Numbers by Monica Yuskaitis.
WARM UP Multiply each Polynomial. 1. (x + 3)(x + 2) 2. (x + 7)(x – 7) 3.5(x + 3) 4. (x + 7)(x – 4) We are simplifying by using the _______________ property.
Exponents. 6³ Exponent Base 6³ is read “Six Cubed” 6³ = 6 x 6 x 6 6³ = 216.
Objective: Add, subtract and multiplying radical expressions; re-write rational exponents in radical form. Essential Question: What rules apply for adding,
Lesson 9-1 Factors and Greatest Common Factors. Definitions Prime Number - A whole number, greater than 1, whose only factors are 1 and itself. Composite.
Objectives The student will be able to: 1. find the prime factorization of a number. 2. find the greatest common factor (GCF) for a set of monomials.
FHSAlgebraic Connections1 Simplifying Radicals NF.4.AC.2: Simplify, add, subtract and multiply radical expressions Students will learn to simplify radicals.
Prime and Composite Factors: – When 2 or more numbers are multiplied, each number is called a factor of the product Ex) 1 x 5 = 52 x 5 = 10 1 x 10 = 10.
Copyright©amberpasillas2010. Parts of a Fraction 3 4 = the number of parts = the total number of parts that equal a whole copyright©amberpasillas2010.
Monomials and Factoring Honors Math – Grade 8. KEY CONCEPT Prime and Composite Numbers A whole number, greater than 1, for which the only factors are.
Copyright©amberpasillas2010. A mixed number has a part that is a whole number and a part that is a fraction. =
Jeopardy Factors, Prime, Composite Prime Factorization Greatest Common Factor Simplifying Fractions Least Common Multiple
Factoring using GCF Algebra I. Definitions Prime number – is a whole number whose only factors are itself and one (a number can’t be factored any more)
Unit 4 Vocabulary Properties of Algebraic Notation.
LESSON #6 Prime and Composite Numbers. PRIME NUMBERS & FACTORS PRIME NUMBER: a number that only has 2 factors (1 and itself) FACTOR: any of the numbers.
LESSON 4-7 EXPONENTS & MULTIPLYING. When we multiply terms with exponents ADD exponents of like variables.
PRIME FACTORIZATION GCF & LCM. FACTORING Factoring is the opposite of multiplying A Factor Times another Factor Equals a Product A Composite Number.
Copyright©amberpasillas2010. For Learning to Happen: Remove all other thoughts from your mind. This lesson is a challenge so please follow along with.
1.7 Simplifying Expressions Essential Questions: 1)What is the distributive property? 2)How do you simplify expressions?
1 ALGEBRA 1B UNIT 8 Multiplication Property of Exponents DAY 2.
Simplifying Radicals Binomial Conjugate:Binomial quantity that turns the expression into a difference of squares.
Slide Copyright © 2009 Pearson Education, Inc. Unit 1 Number Theory MM-150 SURVEY OF MATHEMATICS – Jody Harris.
Prime and Composite Numbers. Prime Numbers- have only 2 factors: 1 and the number itself Composite Numbers- have at least three factors.
Lesson 8.1 Apply Exponent Properties Involving Products After today’s lesson, you should be able to use properties of exponents involving products to simplify.
Factors and Prime Factorization. Definitions Factors ~ Whole numbers that are multiplied to find a product Factors ~ Whole numbers that are multiplied.
Copyright©amberpasillas2010. What does 2 -1 Mean? You cannot leave an exponent negative because there is no way to express it’s meaning.
th Grade Prime Factorization. 2 Vocabulary Product – An answer to a multiplication problem. 7 x 8 = 56 Product.
Opener Evaluate when x = 4.. Test Review Simplifying Exponent Rules.
Copyright©amberpasillas2010. An expression is NOT an equation because it DOES NOT have an equal sign. There are 2 types of expressions Numerical.
Factors and Multiples of Whole Numbers Math 10 Ms. McGrath.
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