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Simplifying Simplifying ExponentsExponents

By By Aditya Bhardwaj, VII BAditya Bhardwaj, VII B

Location of Exponent•An exponent is a little

number high and to the right of a regular or base number.

3 4Base

Exponent

What an Exponent Represents

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

34= 3 x 3 x 3 x 3

How to read an Exponent

•This exponent is read three to the fourth power.

3 4Base

Exponent

How to read an Exponent

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

3 2Base

Exponent

How to read an Exponent

•This exponent is read three to the 3rd power or three cubed.

3 3Base

Exponent

Read These Exponents

3 2 6 72 3 5 4

What is the Exponent?

5 x 5 x 5 x 5 = 5 4

What is the Base and the Exponent?

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

How to Multiply Out an Exponent to Find the

Standard Form

= 3 x 3 x 3 x 33927

81

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What is the Base and Exponent

in Standard Form?

4 2 = 16

What is the Base and Exponent

in Standard Form?

5 3 = 125

Exponents Are Often Used inArea Problems to Show the

Feet Are SquaredLength x width = areaA pool is a rectangleLength = 30 ft.Width = 15 ft.Area = 30 x 15 = 450 ft. 2

15ft.

30ft

Exponents Are Often Used inVolume Problems to Show

theCentimeters Are CubedLength x width x height = volumeA box is a rectangleLength = 10 cm.Width = 10 cm.Height = 20 cm.Volume =

20 x 10 x 10 = 2,000 cm.310

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Multiplication Properties of Exponents

•Product of Powers Property•Power of a Power Property•Power of a Product Property

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Product of Powers Property

• To multiply powers that have the same base, you add the exponents.

• Example: 53232 aaaaaaaaa

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Power of a Power Property

• To find a power of a power, you multiply the exponents.

• Example:

• Therefore,

622222232 )( aaaaaa

63232 )( aaa

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Power of a Product Property

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

• Example: 333333 644)4( zyzyyz

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Write a Number in Scientific Notation

• To write a number in scientific notation, move the decimal to make a number between 1 and 9. Multiply by 10 and write the exponent as the number of places you moved the decimal.

• A positive exponent represents a number larger than 1 and a negative exponent represents a number smaller than 1.

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Scientific Notation• Scientific Notation uses powers of ten to

express decimal numbers.

• For example:

• The positive exponent means that you move the decimal to the right 5 times.

• So,

51039.2

000,2391039.2 5

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Scientific Notation

• If the exponent of 10 is negative, you move the decimal to the left the amount of the exponent.

• Example: 0000000265.01065.2 8

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The End