6-4 Exponents and Division

Geogebra Dividing Powers Division Rule with coefficients

6-4 Videos Divide exponential expressions by noticing patterns In this lesson you will learn how to divide exponential expressions by noticing and generalizing a pattern. Standards: 8.EE.A.1 Apply a zero exponent using patterns and rules In this lesson you will learn how to apply a zero exponent by exploring patterns and making connections to rules you know. Standards: 8.EE.A.1 Apply a negative exponent using patterns and rules In this lesson you will learn how to apply a negative exponent by exploring patterns and making connections to rules you know. Standards: 8.EE.A.1 Simplify expressions with negative exponents In this lesson you will learn how to simplify expressions involving negative exponents by applying exponent rules you already know. Standards: 8.EE.A.1

Divide exponential expressions when exponent in denominator is greate... In this lesson you will learn how to divide expressions where the exponent in the denominator is greater than the exponent in the numerator by applying exponent rules you already know. Standards: 8.EE.A.1 Evaluate expressions with exponents using order of operations In this lesson you will learn how to use the order of operations to evaluate expressions by learning the order then working through examples. Standards: 8.EE.A.1 Simplify expressions with 0 and negative exponents (part 1) In this lesson you will learn how to simplify expressions involving 0 and negative exponents. Standards: 8.EE.A.1 Simplify expressions with 0 and negative exponents (part 2) In this lesson you will learn how to simplify expressions involving 0 and negative exponents. Standards: 8.EE.A.1

Apply exponents to negative bases In this lesson you will learn how to apply exponents to negative bases. Standards: 8.EE.A.1 Divide exponential expressions (part 1) In this lesson you will learn how to divide exponential expressions. Standards: 8.EE.A.1 Divide exponential expressions (part 2) In this lesson you will learn how to divide exponential expressions. Standards: 8.EE.A.1 Evaluate expressions involving exponents In this lesson you will learn how to evaluate expressions involving exponents. Standards: 8.EE.A.1

Video Tutor Help Simplifying when zero is an exponentSimplifying when zero is an exponent (6-4) Simplifying with negative exponentsSimplifying with negative exponents (6-4) Multiplying powers with the same baseMultiplying powers with the same base (6-4b) Exponents and Division Zero as an Exponent Negative Exponents Khan Academy 6-4 Exponents and Division Course 3 Simplifying Divided Exponential Expressions Exponential expressions with divided terms can be simplified using the rules for subtracting exponents. 6-4 Exponents and Division Course 3 Roots and Unit Fraction Exponents Exponents can not only be integers. They can also be fractions. Using the rules of exponents, we can see why a number raised to the power "one over n" is equivalent to the nth root of that number. 6-4 Exponents and Division Course 3 Rational Exponents Exponents can not only be integers and unit fractions. An exponent can be any rational number expressed as the quotient of two integers.

Represent repeated multiplication using exponents In this lesson you will learn how to represent repeated multiplication using an exponent (also called a power) by exploring a model of cell division. Standards: 8.EE.A.1 Apply exponents to negative bases In this lesson you will learn to apply exponents to negative bases by becoming familiar with different notations. Standards: 8.EE.A.1 Multiply two or more exponential expressions In this lesson you will learn how to multiply two or more exponential expressions by exploring and generalizing a pattern Standards: 8.EE.A.1 Raise an exponential expression to a power In this lesson you will learn how to raise an exponential expression to a power by noticing and generalizing a pattern. Standards: 8.EE.A.1 Divide exponential expressions by noticing patterns In this lesson you will learn how to divide exponential expressions by noticing and generalizing a pattern. Standards: 8.EE.A.1

Apply a zero exponent using patterns and rules In this lesson you will learn how to apply a zero exponent by exploring patterns and making connections to rules you know. Standards: 8.EE.A.1 Apply a negative exponent using patterns and rules In this lesson you will learn how to apply a negative exponent by exploring patterns and making connections to rules you know. Standards: 8.EE.A.1 Simplify expressions with negative exponents In this lesson you will learn how to simplify expressions involving negative exponents by applying exponent rules you already know. Standards: 8.EE.A.1 Divide exponential expressions when exponent in denominator is greate... In this lesson you will learn how to divide expressions where the exponent in the denominator is greater than the exponent in the numerator by applying exponent rules you already know. Standards: 8.EE.A.1 Evaluate expressions with exponents using order of operations In this lesson you will learn how to use the order of operations to evaluate expressions by learning the order then working through examples. Standards: 8.EE.A.1

Simplify expressions with 0 and negative exponents (part 1) In this lesson you will learn how to simplify expressions involving 0 and negative exponents. Standards: 8.EE.A.1 Simplify expressions with 0 and negative exponents (part 2) In this lesson you will learn how to simplify expressions involving 0 and negative exponents. Standards: 8.EE.A.1 Apply exponents to negative bases In this lesson you will learn how to apply exponents to negative bases. Standards: 8.EE.A.1 Convert from standard to scientific notation In this lesson you will learn how to convert from standard to scientific notation. Standards: 8.EE.A.1 Multiply numbers expressed in scientific notation In this lesson you will learn how to multiply numbers expressed in scientific notation. Standards: 8.EE.A.1

Simplify exponential multiplication expressions In this lesson you will learn how to simplify exponential multiplication expressions. Standards: 8.EE.A.1 Divide exponential expressions (part 1) In this lesson you will learn how to divide exponential expressions. Standards: 8.EE.A.1 Divide exponential expressions (part 2) In this lesson you will learn how to divide exponential expressions. Standards: 8.EE.A.1 Evaluate expressions involving exponents In this lesson you will learn how to evaluate expressions involving exponents. Standards: 8.EE.A.1

Worksheets 6-4 Note-Taking Guide 6-4 Practice 6-4 Guided Problem Solving

Vocabulary Practice Chapter 6 Vocabulary (Electronic) Flash Cards

Additional Lesson Examples 6-4 Step-by-Step Examples Not found

Lesson Readiness 6-4 Problem of the Day 6-4 Lesson Quiz Not found

Dividing Powers

Division Rule with coefficients

A quotient of powers with the same base can be found by writing the powers in factored form and dividing out common factors. m factors n factors

Simplify. Additional Example 1: Finding Quotients of Powers A.B.

C. Simplify. Additional Example 1: Finding Quotients of Powers D.

Partner Share! Example 1 a. Simplify. b.

Partner Share! Example 1 Simplify. c.d.

Definition of an exponent An exponent tells how many times a number is multiplied by itself. 3 4 = (3)(3)(3)(3) = Base Exponent

How to read an exponent Three to the fourth power 3 4

How to read an exponent (cont’d) Three to the 2 nd power or Three squared 3 2

How to read an exponent (cont’d) Three to the 3rd power or Three cubed 3 3

Exponents are often used in area problems to show the units are squared Area = (length)(width) Length = 30 ft Width = 15 ft Area = (30 ft)(15 ft) = 450 ft 2 15ft 30ft

A = π(8cm) 2 A = 64π cm 2

Exponents are often used in volume problems to show the units are cubed Volume = (length)(width)(height) Length = 10 cm Width = 10 cm Height = 20 cm Volume = (20cm)(10cm)(10cm) = 2,000 cm

What is the exponent? (5)(5)(5)(5) = 5 4

What is the answer? 5 3 = 125

What is the base and the exponent? (7)(7)(7)(7)(7) =7 5

What is the base and the exponent? (x)(x)(x)(x)(x)(x) =x 6

What the base and the exponent? (a)(a)(a)(b)(b)(c) = a 3 b 2 c

Compute: (-4) 2 Answer: (-4)(-4) = 16

Calculate: -4 2 Answer: -(4)(4) = -16 PEMDAS

Simplify: n 2 when n = -5 Answer: (-5) 2 = (-5)(-5) = 25

Simplify: -n 2 when n = -5 Answer: -(-5) 2 = -(-5)(-5) = -25

Compute: (-6) 2 Answer: (-6)(-6) = 36

Compute: -6 2 Answer: -(6)(6) = -36

Compute: -(-6) 2 Answer: -(-6)(-6) = -36

Simplify: (x + 3) 2 Answer: (x + 3)(x + 3) x 2 + 6x + 9

Compute: 0 2 Answer: (0)(0) = 0

Compute: 2 0 Answer: 1 Yes, it’s 1…explanation will follow

WHY is anything to the power zero "1" 3 6 = = = = = = = 1

Laws of Exponents

A monomial is an algebraic expression consisting of only one term. A term may be a number, a variable, or a product or quotient of numbers and variables (separated by a + or –) Examples of monomials: 3, s, 3s, 3sp, 3s 2 p Open Ended: Write 3 different examples of monomials