powerpoint presentation on laws of exponents

My presentations

Presentation on theme: "The Laws of Exponents."— Presentation transcript:

Exponents exponent power base.

Zero Exponent? Product or quotient of powers with the same base? Simplify Negative Exponents.

The Laws of Exponents Animated floating petals (Difficult)

WHEN MULTIPLYING LIKE BASES, YOU ADD THE EXPONENTS FOR EXAMPLE: NOW YOU TRY:

C.L.E.A.R. 15 MINUTES OF READING 5 MINUTES OF QUICKWRITE.

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

Properties of Exponents

WORDS ZERO PRODUCT PROPERTY: A base raised to the power of 0 is equal to 1 NEGATIVE EXPONENT PROPERTY: A negative exponent of a number is equal to the.

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

Multiplication and Division of Exponents Notes

TUESDAY 2.Solve the following equations. a. b. 3.Graph the line. 10x 5 -36x 14 -6r 7 = 13 + r -13 r = – x = -3x + x -8 = -2x x = 4.

Cornell Notes – Topic: Laws of Exponents

Dividing Monomials Chapter 8-2 S. Calahan 2008.

Exponent Properties Product of Powers: 23 ● 22 = 23+2 = 25

About project

Laws of Exponents

Jul 22, 2014

210 likes | 457 Views

Laws of Exponents. Zero Rule. Any non-zero number raised to the zero power equals one X 0 = 1 Examples: 2 0 =1 99 0 = 1. Rule of One. Any number raised to the power of one equals itself. x 1 =x Examples: 17 1 = 17 99 1 = 99.

Share Presentation

quotient rule
negative rule

Presentation Transcript

Zero Rule Any non-zero number raised to the zero power equals one X0 = 1 Examples: 20=1 990= 1

Rule of One Any number raised to the power of one equals itself. x1=x Examples: 171 = 17 991 = 99 Well this one is easy!

Product Rule When multiplying two powers with the samebase, keep the base and add the exponents. xa • xb = xa+b Examples : 42 • 43 = 45 95• 98 = 913 Now here’s a harder one! (x2y4)(x5y6) = x7y10

Quotient Rule When dividing two powers with the same base, keep the base and subtract the exponents. xa÷ xb = xa-b Examples : 75 ÷ 73 = 72 28÷ 22 = 26 Remember that division can also be written vertically: Now here’s a harder one!

But what happens if you add or subtract the exponents and you get a negative number ? First of all, there is no crying in math! Second, we have a law for that too! It’s called the Negative Rule! Let me tell you all about it…

Negative Rule Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power. WHAT!!

…Negative Rule If we apply the negative rule (Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power) then,

Power Rule When raising a power to a power, keep the base and multiply the exponents. (xa)b = xa•b Let me jot this down. Oh yes, I got it now! Examples: (24)3 = 212 (x3)5 = x15

Product to a Power Rule A product raised to a power is equal to each base in the product raised to that exponent. (x• y)2 = x2y2 Examples: (7• 3)2 = 72 •32 = 49 • 9 =441 Here’s one where the variables have exponents Here’s one where the product is raised to a negative power! Tricky, trickier, trickiest – But I think I got it!

(x3y2)5 = x15y10 • (2x2yz-3)-4 = 2-4x-8 y-4 z12 =

Quotient to a Power Rule A quotient raised to a power is equal to each base in the numerator and denominator raised to that exponent. Examples: …and this is the last law!

Example 1- • Simplify

Example 2- Select a strategy to evaluate an expression with 2 variables. Correct Strategy: Simplify first. Then substitute in the value of variables And simplify again

KEY CONCEPTS • Exponent laws are only if the BASES ARE SAME. • It is efficient to SIMPLIFY an algebraic expression before substituting the values of variables. • DONOT CHANGE fractions to decimals to evaluate. [rounding will create errors in answers]

Homework • Page 2 and 3 of your workbook – “Exponents –Multiplying and Dividing”

More by User

Laws of Exponents Practice using PowerPoint

Laws of Exponents. Compute: 25. Answer: 32. Laws of Exponents. Compute: 5-2. Answer: 1/25. Laws of Exponents. Compute: 02. Answer: 0. Laws of Exponents. Compute: 20. Answer: 1. Laws of Exponents. Compute: 00. Answer: ??. Laws of Exponents. Compute: - 42. Answer: -16. Laws of Exponents. C

1.01k views • 25 slides

8.1 Laws of Exponents: Multiplying Monomials

8.1 Laws of Exponents: Multiplying Monomials. Objectives: Define exponents and powers. Find products of powers. Simplify products of monomials.

364 views • 12 slides

Laws of Exponents. x 2 y 4 (xy 3 ) 2. X 2. X 3. Zero Rule. Any non-zero number raised to the zero power equals one X 0 = 1 Examples: 2 0 =1 99 0 = 1. That seems wrong! Anything to the zero power is equal to 1 !?!?.

712 views • 13 slides

The Laws of Exponents : Quotients

The Laws of Exponents : Quotients. #4: Quotient of two powers with equal bases: If you divide the same bases, then subtract the bottom exponent from the top exponent. The Laws of Exponents : Quotients. #5: Power of a quotient: Exponentiation distributes over division.

524 views • 5 slides

The Laws of Exponents

The Laws of Exponents. Exponential Form:. exponent. base. Laws of Exponents:. Multiplying Dividing Power to a Power Zero Power Negative Exponents. 1. Multiplying Exponents. 3 2 × 3 3 = ( 4 3 )(4 4 ) = 6 5 · 6 = Now try these: ( 8 5 )(3 2 ) = 2 3 × 3 2 =.

9.25k views • 18 slides

Laws of Exponents. Whenever we have variables which contain exponents and have the same base, we can do certain mathematical operations to them. Those operations are called the “Laws of Exponents”. b x b = base x = exponent. Laws of Exponents.

1.4k views • 13 slides

Laws of Exponents. Objective: TSW simplify powers. TSW simplify radicals. TSW develop a vocabulary associated with exponents. TSW use the laws of exponents to simplify. Exponents. The lower number is called the base and the upper number is called the exponent.

806 views • 38 slides

Laws of Exponents (with negative exponents)

Laws of Exponents (with negative exponents). BINGO GAME! By Mrs. Math.

1.03k views • 41 slides

5.1 Laws of Exponents

5.1 Laws of Exponents. Ms. Ahearn. GROUPS:. Scientific Notation. How Many Stars in the Universe?. 120,000 LY= Diameter of Milky Way. 13.8 Billion LY = Diameter of Visible Universe. 400 Billion in Milky Way. http:// www.youtube.com/watch?v =WuqB3aB6-RI. Stars in the Solar System?. HMWK:.

243 views • 9 slides

The Laws of Exponents. Exponents. exponent. (Power). base. 5 3 means 3 factors of 5 or 5 x 5 x 5. The Laws of Exponents:. #1: Exponential form: The exponent indicates how many times the base multiplies itself. n factors of x.

1.21k views • 19 slides

Laws of Exponents. Let’s dig deep into our memories and try to remember the laws of exponents. Product Rule. Quotient Rule. It’s all coming back now. I remember this stuff. Laws of Logarithms. What are the Laws of Logarithms?.

2.07k views • 8 slides

Day 1 : Laws of Exponents Review

Day 1 : Laws of Exponents Review. Book sections 7.1 and 7.4. a 0 = 1 b -1 = (a m )(a n ) = a m + n = a m – n (ab) m = a m b m. Do not copy:. Objective: TLW Simplify radicals Simplify with rational exponents

457 views • 19 slides

This powerpoint will help you when working on “ Exponenet Patterning”. Welcome to your personal lesson about the laws of exponents. I hope you enjoy your experience! Here are some things you need to know:

1.16k views • 74 slides

Laws of Exponents. 7-2 through 7-4. What we call expanded notation. What we call expanded notation. What we call expanded notation. Putting it all together…. Putting it all together… =3  3  3  3  3  3. Putting it all together… =3  3  3  3  3  3

2.26k views • 205 slides

Powers and Laws of Exponents

Powers and Laws of Exponents.

679 views • 6 slides

Laws of Exponents. By Chancy Nordick. Review. What exactly is a power function again?. A power function has two parts:. Exponent. Base. Review Continued. Where. And. Multiplication Laws. What if we want to multiply two power functions?. Example:. Multiplication Laws. In General.

621 views • 39 slides

The Laws of Exponents. Exponents. exponent. Power. base. 5 3 means 3 factors of 5 or 5 x 5 x 5. The Laws of Exponents:. #1: Exponential form: The exponent of a power indicates how many times the base multiplies itself. n factors of x.

573 views • 19 slides

Self-learning study material

100 views • 7 slides

266 views • 19 slides

Laws of Exponents. Vocabulary. Factor: an integer that divides into another integer with no remainder. 24. 1, 2, 3, 4, 6, 8, 12, 24. Exponent: tells how many times to multiply a number by itself Base: the number that is multiplied by itself

373 views • 8 slides

The Laws of Exponents. Exponents. exponent. Power. base. 5 3 means 3 factors of 5 or 5 x 5 x 5. The Laws of Exponents:. Exponential form: The exponent of a power indicates how many times the base multiplies itself. n factors of x.

786 views • 19 slides

8.1 Laws of Exponents

8.1 Laws of Exponents. Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are called the “Laws of Exponents”. b x b = base x = exponent. Laws of Exponents.

620 views • 21 slides

Preferences

Laws of Exponents - PowerPoint PPT Presentation

Laws of Exponents

Laws of exponents goal to write simplified statements that contain distinct bases, one whole number in the numerator and one in the denominator, and no negative ... – powerpoint ppt presentation.

BaseExponent
Base raised to an exponent
To write simplified statements that contain distinct bases, one whole number in the numerator and one in the denominator, and no negative exponents.
This power point will address the laws of exponents in the following manner
Explore how the rule works.
State the rule.
Provide an example with a solution.
Provide extra examples (Find me to get solutions)
Evaluate the following without a calculator
Describe a pattern and find the answer for
Simplify the following expressions

PowerShow.com is a leading presentation sharing website. It has millions of presentations already uploaded and available with 1,000s more being uploaded by its users every day. Whatever your area of interest, here you’ll be able to find and view presentations you’ll love and possibly download. And, best of all, it is completely free and easy to use.

You might even have a presentation you’d like to share with others. If so, just upload it to PowerShow.com. We’ll convert it to an HTML5 slideshow that includes all the media types you’ve already added: audio, video, music, pictures, animations and transition effects. Then you can share it with your target audience as well as PowerShow.com’s millions of monthly visitors. And, again, it’s all free.

About the Developers

PowerShow.com is brought to you by CrystalGraphics , the award-winning developer and market-leading publisher of rich-media enhancement products for presentations. Our product offerings include millions of PowerPoint templates, diagrams, animated 3D characters and more.

World's Best PowerPoint Templates PowerPoint PPT Presentation

Laws of Exponents

Exponents are also called Powers or Indices

The exponent of a number says how many times to use the number in a multiplication.

In this example: 8 2 = 8 × 8 = 64

Try it yourself:

So an Exponent saves us writing out lots of multiplies!

Example: a 7

a 7 = a × a × a × a × a × a × a = aaaaaaa

Notice how we wrote the letters together to mean multiply? We will do that a lot here.

Example: x 6 = xxxxxx

The key to the laws.

Writing all the letters down is the key to understanding the Laws

Example: x 2 x 3 = (xx)(xxx) = xxxxx = x 5

Which shows that x 2 x 3 = x 5 , but more on that later!

So, when in doubt, just remember to write down all the letters (as many as the exponent tells you to) and see if you can make sense of it.

All you need to know ...

The "Laws of Exponents" (also called "Rules of Exponents") come from three ideas :

The exponent says to use the number in a multiplication

A means , because the opposite of multiplying is dividing

A like means to :

x ) = n√x

If you understand those, then you understand exponents!

And all the laws below are based on those ideas.

Here are the Laws (explanations follow):

Law	Example
x = x	6 = 6
x = 1	7 = 1
x = 1/x	4 = 1/4

x x = x	x x = x = x
x /x = x	x /x = x = x
(x ) = x	(x ) = x = x
(xy) = x y	(xy) = x y
(x/y) = x /y	(x/y) = x / y
x = 1/x	x = 1/x
And the law about Fractional Exponents:
x = n√x = (n√x )	x = 3√x = (3√x )

Laws Explained

The first three laws above ( x 1 = x , x 0 = 1 and x -1 = 1/x ) are just part of the natural sequence of exponents. Have a look at this:

Example: Powers of 5
	.. etc..
		25
		5
		1
		0.2
		0.04
	.. etc..

Look at that table for a while ... notice that positive, zero or negative exponents are really part of the same pattern, i.e. 5 times larger (or 5 times smaller) depending on whether the exponent gets larger (or smaller).

The law that x m x n = x m+n

With x m x n , how many times do we end up multiplying "x"? Answer: first "m" times, then by another "n" times, for a total of "m+n" times.

So, x 2 x 3 = x (2+3) = x 5

The law that x m /x n = x m-n

Like the previous example, how many times do we end up multiplying "x"? Answer: "m" times, then reduce that by "n" times (because we are dividing), for a total of "m-n" times.

Example: x 4 /x 2 = (xxxx) / (xx) = xx = x 2

So, x 4 /x 2 = x (4-2) = x 2

(Remember that x / x = 1, so every time you see an x "above the line" and one "below the line" you can cancel them out.)

This law can also show you why x 0 =1 :

Example: x 2 /x 2 = x 2-2 = x 0 =1

The law that (x m ) n = x mn.

First you multiply "m" times. Then you have to do that "n" times , for a total of m×n times.

Example: (x 3 ) 4 = (xxx) 4 = (xxx)(xxx)(xxx)(xxx) = xxxxxxxxxxxx = x 12

So (x 3 ) 4 = x 3×4 = x 12

The law that (xy) n = x n y n

To show how this one works, just think of re-arranging all the "x"s and "y"s as in this example:

Example: (xy) 3 = (xy)(xy)(xy) = xyxyxy = xxxyyy = (xxx)(yyy) = x 3 y 3

The law that (x/y) n = x n /y n.

Similar to the previous example, just re-arrange the "x"s and "y"s

Example: (x/y) 3 = (x/y)(x/y)(x/y) = (xxx)/(yyy) = x 3 /y 3

The law that x m/n = n √ x m = ( n √ x ) m.

OK, this one is a little more complicated!

I suggest you read Fractional Exponents first, so this makes more sense.

Anyway, the important idea is that:

x 1/ n = The n- th Root of x

And so a fractional exponent like 4 3/2 is really saying to do a cube (3) and a square root (1/2), in any order.

Just remember from fractions that m/n = m × (1/n) :

Example: x ( m n ) = x (m × 1 n ) = (x m ) 1/n = n √ x m

The order does not matter, so it also works for m/n = (1/n) × m :

Example: x ( m n ) = x ( 1 n × m) = (x 1/n ) m = ( n √ x ) m

Exponents of exponents ....

What about this example?

We do the exponent at the top first , so we calculate it this way:

Start with:		4
3 = 3×3:		4
4 = 4×4×4×4×4×4×4×4×4:		262144

And That Is It!

If you find it hard to remember all these rules, then remember this:

you can work them out when you understand the three ideas near the top of this page:

The exponent says how many times to use the number in a multiplication
A negative exponent means divide
A fractional exponent like 1/n means to take the nth root : x ( 1 n ) = n √ x

Oh, One More Thing ... What if x = 0?

Positive Exponent (n>0)		0 = 0
Negative Exponent (n<0)		0 is (because is undefined)
Exponent = 0		0 ... ... see below!

The Strange Case of 0 0

There are different arguments for the correct value of 0 0

0 0 could be 1, or possibly 0, so some people say it is really "indeterminate":

	x = 1, so ...	0 = 1
	0 = 0, so ...	0 = 0
	When in doubt ...	0 =

COMMENTS

PPT
The Laws of Exponents : Quotients. The Laws of Exponents : Quotients. #4: Quotient of two powers with equal bases: If you divide the same bases, then subtract the bottom exponent from the top exponent. The Laws of Exponents : Quotients. #5: Power of a quotient: Exponentiation distributes over division. 521 views • 5 slides
PPT
The Laws of Exponents. Exponents exponent Power base 53 means 3 factors of 5 or 5 x 5 x 5. The Laws of Exponents: Exponential form:The exponent of a power indicates how many times the base multiplies itself. n factors of x. #1: Multiplying Powers (Product of Powers): If you are multiplying Powers with the same base, KEEP the BASE & ADD the ...
PPT
Laws of Exponents. Laws of Exponents. Whenever we have variables which contain exponents and have the same base, we can do certain mathematical operations to them. Those operations are called the "Laws of Exponents". b x b = base x = exponent. Laws of Exponents. 1.39k views • 13 slides
The Laws of Exponents.
Download presentation. Presentation on theme: "The Laws of Exponents."—. Presentation transcript: 1 The Laws of Exponents. 2 Exponents exponent Power base 53 means 3 factors of 5 or 5 x 5 x 5. 3 #1: Exponential form: The exponent of a power indicates. The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many ...
Laws of Exponents
Title: Laws of Exponents. Description: Laws of Exponents Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are ... - PowerPoint PPT presentation. Number of Views: 405. Avg rating:3.0/5.0. Slides: 9.
PDF Laws of Exponents
Laws of Exponents. Lesson 2. Law 4: Zero Exponent. Click on the link below for a video on the Zero Exponent. ... When the video is finished, please return to the PowerPoint presentation. Some Practice Problems • Simplify fully (write without negative exponents): Answers to Practice Problems.
Law Of Exponents Ppt Teaching Resources
This 30 slide Powerpoint presentation contains instruction, examples, and practice problems with answer keys on the next slide. The slides are grouped: exponents with numerical bases, laws of exponents with products and quotients, power rules for products, and quotients, zero and negative exponents.
PPT
Presentation Transcript. Laws of Exponents. Zero Rule Any non-zero number raised to the zero power equals one X0 = 1 Examples: 20=1 990= 1. Rule of One Any number raised to the power of one equals itself. x1=x Examples: 171 = 17 991 = 99 Well this one is easy! Product Rule When multiplying two powers with the samebase, keep the base and add the ...
Sixth Grade Laws of Exponents PowerPoint & Google Slides
This resource, Sixth Grade Laws of Exponents PowerPoint & Google Slides, is an excellent way to engage your students in learning about the laws of exponents. Throughout the PowerPoint, there is an opportunity for your students to collaborate and practice problems, engaging them in the lesson each step of the way! After you're finished with this PowerPoint, why not choose some more ...
Laws of Exponents
About This Presentation. Title: Laws of Exponents. Description: Laws of Exponents Goal To write simplified statements that contain distinct bases, one whole number in the numerator and one in the denominator, and no negative ... - PowerPoint PPT presentation. Number of Views: 235. Avg rating:3.0/5.0. Slides: 31.
Laws of Exponents
Laws of Exponents. Exponents are also called Powers or Indices. The exponent of a number says how many times to use the number in a multiplication. In this example: 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the second power", "8 to the power 2" or simply "8 squared". Try it yourself:
PDF Laws of Exponents
Laws of Exponents Lesson 1. Law 1: Product Rule Click on the link below for a video on the product rule. ... When the video is finished, please return to the PowerPoint presentation. Some Practice Problems •Simplify fully: Answers to Practice Problems. Summary of Rules Learned •Product Rule: •Quotient Rule:
LAWS OF EXPONENT
For today's topic, we are going to talk about the "Law of Exponents".In our previous video, we already define what is exponent all about. If you haven't watc...