Basics about exponents

Exponents are a shorthand way to

show a larger number.

What is an exponent?

Exponents are sometimes referred to as “powers.”

Where is an exponent located at?

64Base Exponent

How do you read an exponent?

A number with an exponent is said to be

"raised to the power" of that exponent.

Let’s look at some examples. . . .

32 = three raised to the second power or three

squared53 = five raised to the third

power or five cubed

74 = seven raised to the fourth power

What does an exponent mean?

We will use an example of how the secret spread fast to explain what does an exponent mean.

How does a secret spread so fast?

• The person with a secret tells a friend.

• The friend promises never to tell anyone.

• That same friend breaks the promise and tells two more friends.

• The two new friends tell two new friends.

•The two new friends decide to tell two more friends.

•This pattern occurs over and over until many people have been told.

•By the end of the day it is no longer a secret!

Here is how a secret can spread

Round 1 Round 2

I have a secret and I tell 3 of my best friends.

My 3 friends each tell 3 more people.

Look how many people now know the secret!

3 x 3 = 9

9 people know!

In an exponential expression, the base is the factor, and the exponent tells the amount of

times to multiple that number by itself. (That is a mouthful!)

34

Your BASE = 3 Your EXPONENT = 4

• A base is a number that can be expressed using an exponent.

• An exponent is the small number and is referred to as a “power.”

34 means 3 x 3 x 3 or 27

LAWS OF EXPONENTS

• Recall: A number in exponential form has a base and an exponent. The exponent indicates how many times the base is used as a factor.

• In its exponential form: ab

a is the BASE and b is the EXPONENT.

NOTES

The laws of exponents show how to

SIMPLIFY

expressions in exponential form.

NOTES

In the next few slides, a and b are real numbers and m and n are

integers.

Product of powers

• To multiply powers with the same base, add the exponents.

am ∙an = am+n

3 4 3 4 7Example: 2 2 2 2

3 4

7

Proof: 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2

Power of a power

• To raise a number in exponential form to a power, multiply the exponents.

(am)n = am∙n

23 3 2 6Example: 4 4 4

Power of a product

• To find a power of a product, find the power of each factor and multiply.

(ab)m = ambm

22 2

2 2

2

Proof: 2 3 4 9

Example: 36 6 2 3 2 3

36

Power of zero

• Any nonzero number raised to the power of zero is one.

a0 = 1

Quotient of powers

• To find the quotient of powers with the same base, subtract the exponents.

am = am-n

an

•For example…

32 ÷ 32 = 3 2 - 2 = 30

32 = 3 3 = 9 = 1

32 3 3 9

Power of a quotient

To raise a quotient to a power, raise both the numerator and denominator to that power.

(a/b)m = am/bm

3 3

3

2 2Example:

7 7

Reciprocals

• To change a sign of an exponent, move the expression to the denominator of a fraction, or to the numerator.

a-n = 1/an

1/a-n = an

33

1 1Example #1: 2

2 8

33

3

1 5Example #2: 5 125

5 1

referencesMaslijr, 2013, Laws of exponents, viewed 05 March 2014, from http://www.slideshare.net/masljr/laws-of-exponents-23863798

Melnichenko, Y., 2008, Exponents, viewed 05 march 2014, from http://www.slideshare.net/yelena585/exponents-presentation?qid=c977ae81-f7bd-48bf-bf86-c88dd4657047&v=default&b=&from_search=30

Morris, B., 2012, Grade 6 exponents lesson, viewed 05 March 2014, from http://www.slideshare.net/BobMorris72/math-exponents?qid=c977ae81-f7bd-48bf-bf86-c88dd4657047&v=default&b=&from_search=2

Scallion, K., 2010, Rules of exponents, viewed 05 March 2014, from http://www.slideshare.net/kscallion/rules-of-exponents

Wilkerosn,K., 2013, Exponents, viewed 05 march 2014, from http://www.slideshare.net/katiewilkerosn/exponents-27460394?qid=c977ae81-f7bd-48bf-bf86-c88dd4657047&v=default&b=&from_search=11

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