ExponentsExponents- An introduction -

By Carol EdelsteinDavid E. Owens Middle School

New Milford, NJ

Location of an ExponentLocation of an Exponent

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

3 4 Base

Exponent

Definition of ExponentDefinition of Exponent An exponent tells you how many times An exponent tells you how many times

the base number is multiplied by itself. the base number is multiplied by itself.

34

BaseExponent

So, 3So, 344 is equal to 3 x 3 x 3 x is equal to 3 x 3 x 3 x 3. 3.

How to read an ExponentHow to read an Exponent

This exponent is read “three to This exponent is read “three to the fourth power”the fourth power”..

34

This exponent is read “two to This exponent is read “two to the sixth power”the sixth power”..

26

How to read an Exponent How to read an Exponent (the special cases)(the special cases)

This exponent is read “seven to the This exponent is read “seven to the second power”second power” or or “seven squared”“seven squared”..

7 2

This exponent is read “eight to the This exponent is read “eight to the third power”third power” or or “eight cubed”“eight cubed”..

83

Practice – Practice – Read These ExponentsRead These Exponents

3 2 6 72 3 5 4

Did you get…Did you get…

3 2 6 72 3 5 4

Two to the third power Seven to the fourth power

or Two cubed

Three to the second power

or Three squared Six to the fifth power

What is the Exponent?What is the Exponent?

2 x 2 x 2 = 23

What is the Exponent?What is the Exponent?

3 x 3 = 3 2

What is the Exponent?What is the Exponent?

5 x 5 x 5 x 5 = 54

What is the Base and What is the Base and the Exponent?the Exponent?

8 x 8 x 8 x 8 = 8 4

What is the Base and What is the Base and the Exponent?the Exponent?

7 x 7 x 7 x 7 x 7 =7 5

What is the Base and What is the Base and the Exponent?the Exponent?

9 x 9 = 9 2

How to multiply out an How to multiply out an Exponent to find theExponent to find the

Standard FormStandard Form

= 3 x 3 x 3 x 33

927

81

4

4 2= 16

4 x 4 = 16

Write the Power in Write the Power in Standard FormStandard Form

Make sure that you do

not read this question as 4 x 2.

Write the Power in Write the Power in Standard FormStandard Form

2 3= 8

2 x 2 x 2 =

4 x 2 = 8

How did you do?

3 2= 9

3 x 3 = 9

Write the Power in Write the Power in Standard FormStandard Form

Again, make sure that you

do not read this question as 3 x 2.

5 4= 625

5 x 5 x 5 x5 =

25 x 5 x 5 =

125 x 5 = 625

Write the Power in Write the Power in Standard FormStandard Form

Exponents used inExponents used inArea ProblemsArea Problems

Area = length x width

Length = 30 ft Width = 15 ft

Area = 30 ft x 15ft = 450 ft 2

15ft

30ft

Remember: ft 2 = ft x ft

Exponents are used Exponents are used inin

Volume ProblemsVolume ProblemsVolume = length x width x height

length = 10 cm width = 10 cm height = 20 cm

Volume = 20 cm x 10 cm x 10 cm = 2,000 cm 3

10cm10cm

20cm

Remember: cm3 = cm x cm x cm

Exponents are also Exponents are also used…used…

in in scientific notationscientific notation to express very to express very large large oror small numbers. small numbers.

Example:Example:

The distance to the sun is about 90,000,000 The distance to the sun is about 90,000,000 miles. miles.

Using scientific notation, we can write this Using scientific notation, we can write this number. number.

90,000,000 = 9 x 10 x 10 x 10 x 10 x 10 x 10 x 90,000,000 = 9 x 10 x 10 x 10 x 10 x 10 x 10 x 1010

9 x 10 9 x 10 77

Scientific notation

The EndThe End

Congratulations, now you know a little more about exponents.