Exponents

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4 Exponent 3 Base Base - the repeated factor; the Big, Bottom number; the only number you may write as a factor. tells you how many times to use the base as a repeated factor. Exponent-

What an Exponent Represents 4 3 = 3 x 3 x 3 x 3 exponential form product of repeated (equal) factors (expanded form)

three to the fourth power How to read an Exponent 4 3 three to the fourth power

three to the 3rd power or three cubed 2 three to the 2nd power or three squared 3 3 three to the 3rd power or three cubed

2 6 7 8 2 5 3 4 eight squared two cubed six to the fifth power Read These Exponents 2 2 6 5 7 8 3 4 eight squared two cubed six to the fifth power seven to the fourth power

What is the Exponent? 2 x 2 x 2 = 3 2 2 3 x 3 = 3 4 5 x 5 x 5 x 5 = 5

What is the Base and the Exponent? 4 8·8·8·8 = 8 7·7·7·7·7 = 7 5 9 2 9·9 =

How to evaluate an exponent by multiplying out. 4 3 = 3 x 3 x 3 x 3 9 27 81

2 16 4 = Evaluate: 3 2 9 = 4 16 2 = 3 125 5 =

1 raised to any power will always be 1. A Few to Memorize!!! 1 raised to any power will always be 1. 3 1 1 = 1 = 1 15 1,309 1 = 1

5 = 1 1 8 = 1 23 = Any number raised to the power of zero will always be one. 5 = 1 1 8 = 1 23 =

16 8 4 2 1 Proof: 2 = 2³ = 2² = 2¹ = 2° = See a pattern? How does that work? Proof: 2 = 2³ = 2² = 2¹ = 2° = 16 8 4 See a pattern? 2 1

5 = 5 15 = 15 8 = 8 Any number raised to the power of one will always be itself. 5 = 1 5 1 15 = 15 1 8 = 8

Base 10 An exponential expression with a base of ten can be evaluated by writing the number 1 followed by a number of zeros that match the exponent. 2 = 100 10 5 = 100,000 10

area = length x width A pool is a rectangle Length = 30 ft. Exponents Are Often Used in Area Problems to Show the units Are Squared area = length x width A pool is a rectangle Length = 30 ft. Width = 15 ft. A = 30ft x 15ft = 450 ft 15ft. 30ft 2

Volume = length x width x height A box is a rectangle Length = 10 cm Exponents Are Often Used in Volume Problems to Show the units Are Cubed Volume = length x width x height A box is a rectangle Length = 10 cm Width = 10 cm Height = 20 cm Volume = 10cm x 10cm x 20cm = 2,000 cm 20 10 10 3

Here Are Some Areas Change Them to Exponents 2 40 feet squared = 40 ft 56 sq. inches = 56 in 38 m squared = 38 m 56 sq. cm = 56 cm 2 2 2

Here Are Some Volumes Change Them to Exponents 3 30 feet cubed = 30 ft 26 cu. inches = 26 in 44 m cubed = 44 m 56 cu. cm = 56 cm 3 3 3