6-2 Exponents and Multiplication

Geogebra Multiplying Powers Product Rule with Negatives Power of a Power Rule

6-2 Videos 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

Apply exponents to negative bases In this lesson you will learn how to apply exponents to negative bases. 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 Evaluate expressions involving exponents In this lesson you will learn how to evaluate expressions involving exponents. Standards: 8.EE.A.1

Video Tutor Help Using properties of multiplicationUsing properties of multiplication (6-2) Exponents and Multiplication Multiplying Powers Khan Academy 6-2 Exponents and Multiplication Course 3 Exponentiation Exponentiation is shorthand for repeated multiplication, just like multiplication is shorthand for repeated addition. Multiplied or divided exponential terms with like bases can be combined by adding or subtracting their exponents. 6-2 Exponents and Multiplication Course 3 Exponents of One, Zero, and Negative Integer exponents greater than one represent the number of copies of the base which are multiplied together. But what if the exponent is one, zero or negative? Using the rules of adding and subtracting exponents, we can see what the meaning must be. 6-2 Exponents and Multiplication Course 3 Simplifying Multiplied Exponential Expressions Exponential expressions with multiplied terms can be simplified using the rules for adding exponents. 6-2 Exponents and Multiplication Course 3 Simplifying Mixed Exponential Expressions Exponential expressions with multiplied and divided terms can be simplified using the rules of adding and subtracting exponents.

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 6-2 Note-Taking Guide 6-2 Practice 6-2 Guided Problem Solving

Vocabulary Practice Chapter 6 Vocabulary (Electronic) Flash Cards

Additional Lesson Examples 6-2 Step-by-Step Examples Not found

Lesson Readiness 6-2 Problem of the Day 6-2 Lesson Quiz Not found

Multiplying Powers

Power of a Power Rule

Product Rule with Negatives

Products of powers with the same base can be found by writing each power as a repeated multiplication. a m  a n = (a  a  …  a)  (a  a  …  a) m factors n factors = a  a  …  a = a m+n m + n factors

Simplify. Additional Example 1: Finding Products of Powers A. Since the powers have the same base, keep the base and add the exponents. B. Group powers with the same base together. Add the exponents of powers with the same base.

Simplify. Additional Example 1: Finding Products of Powers C. D. n 0 1, only if n≠0 Group powers with the same base together. Add the exponents of powers with the same base. The first two powers have the same base, so add the exponents. Add the exponents. Group the first two powers.

A number or variable written without an exponent actually has an exponent of 1. Remember! 10 = 10 1 y = y 1

Partner Share! Example 1 a. Simplify. Since the powers have the same base, keep the base and add the exponents. b. Group powers with the same base together. Add the exponents of powers with the same base.

Partner Share! Example 1 Simplify. c. Group powers with the same base together. Add.

Partner Share! Example 2 Light travels at about 1.86 × 10 5 miles per second. Find the approximate distance that light travels in one hour. Write your answer in scientific notation. distance = rate  time Write 3,600 in scientific notation. Multiply within each group. Use the Commutative and Associative Properties to group. Light will travel × 10 8 miles in one hour.

To find a power of a power, you can use the meaning of exponents. n factors = a  a  …  a  a  a  …  a  …  a  a  …  a = a mn = a m  a m  …  a m m factors n groups of m factors

Simplify. Additional Example 3: Finding Powers of Powers Use the Power of a Power Property. Simplify. 1 Use the Power of a Power Property. Zero multiplied by any number is zero. Any non-zero number raised to the zero power is 1.

Simplify. Additional Example 3: Finding Powers of Powers Use the Power of a Power Property. Simplify the exponent of the first term. Since the powers have the same base, add the exponents. Write with a positive exponent. C.

Partner Share! Example 3 Simplify. Use the Power of a Power Property. Simplify. 1 Use the Power of a Power Property. Zero multiplied by any number is zero. Any number raised to the zero power is 1.

Partner Share! Example 3c Simplify. Use the Power of a Power Property. Simplify the exponents of the two terms. Since the powers have the same base, add the exponents. c.

Powers of products can be found by using the meaning of an exponent. (ab) n = ab  ab  …  ab n factors = a  a  …  a  b  b  …  b = a n b n n factors

Additional Example 4: Finding Powers of Products Simplify. Use the Power of a Product Property. Simplify. Use the Power of a Product Property. Simplify. A. B.

Caution! In Example 4A, the negative sign is not part of the base. –(2y) 2 = –1  (2y) 2

Additional Example 4: Finding Powers of Products Simplify. Use the Power of a Product Property. Use the Power of a Power Property. Simplify. C.

Partner Share! Example 4 Simplify. Use the Power of a Product Property. Simplify. Use the Power of a Power Property. Simplify.

Partner Share! Example 4 Simplify. Use the Power of a Product Property. Use the Power of a Power Property. Simplify. Write with a positive exponent. c.

Lesson Review: Part I Simplify (x3)2(x3)2

Lesson Review: Part II 8. The islands of Samoa have an approximate area of 2.9  10 3 square kilometers. The area of Texas is about 2.3  10 2 times as great as that of the islands. What is the approximate area of Texas? Write your answer in scientific notation × 10 5 km 2