1 Simplifying Simplifying Exponents Exponents By By Aditya Bhardwaj, VII B Aditya Bhardwaj, VII B
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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
4
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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10
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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
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