Exponents

For Learning to Happen!

•Remove all other thoughts from your mind.•Pay close attention to this lesson.•Try all of the examples.•Ignore all other distractions.

An exponent is a little number high and An exponent is a little number high and to the right of a regular or base number.to the right of a regular or base number.

BaseExponent

This exponent is read This exponent is read

8 to the 3rd power, 8 to the 3rd power,

or 8 cubed.or 8 cubed.

BaseExponent

An exponent tells how An exponent tells how many times a number is many times a number is multiplied by itself. multiplied by itself.

BaseExponent

This exponent means This exponent means

8•8•8 = 512

This exponent is read This exponent is read

six to the fourth power.six to the fourth power.

6 4Base

Exponent

This exponent is read This exponent is read three to the 2three to the 2ndnd power or power or three squared.three squared.

3 2Base

Exponent

Read These Exponents

77 to the 2nd poweror 7 squared

Read These Exponents

1010 to the 3rd poweror 10 cubed

What is the Exponent?

2 • 2 • 2 = 23

a • a • a • a = a4

(bc)(bc)(bc) = (bc)3

NOTICE that you keep the parenthesis around the variables (bc) because you

are cubing all the (bc)

Write the Verbal PhasePower Verbal Phrase Means

27 “Seven to the 2nd power” 7 7“Seven squared”

35 “Five to the 3rd power” 5 5 5 “Five cubed”

Write the Verbal PhasePower Verbal Phrase Meaning

49 “Nine to the 4th power” 9 9 9 9

52 “Two to the 5th power”2 2 2 2 2

How to Multiply Out Exponents

= 3 • 3 • 3 • 33

How to Multiply Out Exponents

= 2 • 2 • 2 • 2 • 22

When simplifying exponents you must watch the sign and the parenthesis!

= 6•6 = 36

= –6•6 = -36

=(-6)(-6) = 36

= - (6)(6)1 = -36

An exponent is written in An exponent is written in exponential formexponential form when it is when it is simplified.simplified.

3322aa

Exponential Form

An exponent is written in An exponent is written in factor formfactor form when it is written when it is written out. out.

3322aa

33= 3•3•a•a•a

Factor Form

Factored Form Exponential Form

x • 8 • y • 8 • x 82x

a • b • a • 2 2a2b

13 p p p r r 13p3r2

5 • x • x • x 5x3

(5x)3 (5x)(5x)(5x) = 53x3

= 125x3

8(ab)(ab) 8(ab)2

= 43x3w3y3(4xwy)3 (4xwy)(4xwy)(4xwy)

= 8a2b2

= 64x3w3y3

Evaluate the expression if x = 3 and y = 4

2 2x +y2 23 +4

“Evaluate” mean to solve!

9 + 16

Evaluate the expression if x = 3 and y = 4

22(x+y)22(3+4)

“Evaluate” mean to solve!

Fractions With Exponents2

1 1 1 1

2 2 2 2

Fractions With Exponents

2 23 3

1 15 5 1

Fractions With Exponents

3 37 7

2 2 26 6 6

Take out your Study Guide (blue).

An exponent tells how many times a number is multiplied by itself.

83Base

Exponent

Factored Form

3 • 3 • a • a • a

Exponential Form

x • y • x • 2 2x

8•8•8 = 512

2 23 3 4

# 2When simplifying exponents you must watch the sign and the parenthesis!

= 5•5 = 25

= – (5)•(5) = –25

=(-5)(-5) = 25 –(5)2

= - (5)(5) = –251

5 5 25

2 2 2 2 16

10 10 10 1000

12 12 144

To find 54 on my calculator I type in 5 4^ = 625

5 yx 4 = 625

5 4 = 625

Circle the method that works on your calculator!

TEACHER NOTE: The lesson above was taught for Pre-Algebra &

Algebra.

The following slides were used for the class of Algebra Readiness

(lower level students) and slide #18-28 were taken out of the

lesson above since we were just introducing Exponents.

Evaluate the Power“Evaluate” mean to solve!

5 5 25

2 2 2 2 16

10 10 10 1000

12 12 144

7 units3

Addition:-One-Dimensional Growth

+ =+ 4 =

Multiplication: Two-Dimensional Growth

“Three added to four”

“Three times four” or “Three groups of four”

+4 +4 4= 12 square units3(4)=

Multiplication is Repeated Addition

Exponents: Three-Dimensional Growth

“Three to the third power”“Three to the fourth power”

3 33 33 3 3 3

327 un

43 3 3 3 3 381 un

Exponents is Repeated Multiplication

Perimeter Area Volume 5

P = s+s+s+sP = 4s

P=4 5P=20 units

2A =s2A =5

A =25 2units

3V =s3V =5

V =125 3units

OneDimensional

TwoDimensional

ThreeDimensional

“Five Squared” “Five Cubed”

I am going to give you a Study Guide (blue).Please take good notes on what we just learned! You can use these notes to help you with homework! You can use these notes on your test!

Exponents & PowersAn exponent or power tells how manytimes a number is multiplied by itself.

BaseExponent

25 “Five to the 2nd power” 5 5“Five squared”

37 “Seven to the 3rd power” 7 7 7 “Seven cubed”

5 5 25

2 2 2 2 16

10 10 10 1000

12 12 144

To find 54 on my calculator I type in 5 4^ = 625

5 yx 4 = 625

5 4 = 625

Circle the method that works on your calculator!

Exponents

Documents

44 exponents

Solving Exponents

Lesson Menu Main Idea Key Concept:Negative Exponents Example 1:Use Positive Exponents Example 2:Use Positive Exponents Example 3:Use Negative Exponents

EXPONENTS ROOTS Review packet Exercises - Hanlon … · Exponents & Roots – Review Packet – Exercises Hanlonmath.com 1 BASICS OF EXPONENTS Rewrite, using exponents. 1. 5 x 5 x

Module 4 Zero Exponents, Negative Integral Exponents ... · PDF file09.02.2015 · Table of Contents Module 4. Zero Exponents, Negative integral Exponents, Rational Exponents, and

Exponents and Polynomials - Whitesboro Central School … · 2015-07-31 · Exponents and Polynomials 7A Exponents 7-1 Integer Exponents ... EXAMPLE 2 Zero and Negative Exponents

10.1 INTEGER EXPONENTS 10 2 FRACTIONAL EXPONENTS 10.2

Exponents Roots

Exponents lesson 6 day 2 zero and negative exponents

· Graphic Organizer: Properties Of Exponents EXPONENTS x is called the PROPERTIES OF EXPONENTS 8.2 - Olvislon Properties bas* that are the : Same, you exponents 8.3 —Zero and

COLLEGE ALGEBRA - WichitaInteger Exponents – In this section we will start looking at exponents and their properties. Rational Exponents – We will define rational exponents in

Rational Exponentslehimath.weebly.com/.../lesson_4.4_rational_exponents.pdfAll the properties of integer exponents apply to rational exponents. Properties Properties of Rational Exponents

Chapter 1 Exponents (Laws of Exponents)

Multiplying Exponents

Exponents and RootsExponents and Rootsmathwithmrbarnes.weebly.com/uploads/1/1/2/1/... · 4A Exponents 4-1 Exponents 4-2 Integer Exponents 4-3 Properties of Exponents 4-4 Multiplying

Unit 2: Exponents · 2015-01-30 · with exponents. •When multiplying, add the exponents •When dividing, subtract the exponents •Power to a power requires multiplying the exponents

Welcome to Unit 5 Our Topics for this week Radical Exponents – Review Rules for Exponents – Zero exponents – Negative Exponents Rational Expressions Simplifying

+ Exponents I can write numerical expressions involving whole number exponents

Chapter 8 Review Game Exponents Evaluating with Exponents Simplifying with Exponents Scientific Notation Exponential Growth and Decay

6.1 Multiplication with Exponents and Scientific Notation 6.2 Division with Exponents and Negative Exponents 6.3 Operations with Monomials