Exponents Exponents and Powersand Powers

3344

3 3 × 3 × 3 × 3× 3 × 3 × 3

9 × 99 × 9

8181

Write each product using Write each product using exponent exponent form.form.

1.1. 11 11 × 11 × 11× 11 × 1111³11³

2.2. 15 × 15 × 8 × 815 × 15 × 8 × 815²15² × 8² × 8²

Evaluate each expression. Find the Evaluate each expression. Find the standard formstandard form..

5.5. 3 squared3 squared3322

3 3 × 3 × 3 9 9

6. 6. 442 2 × 3× 333

4 × 4 × 3 × 3 × 34 × 4 × 3 × 3 × 3 16 × 2716 × 27

432432

Exponent Exponent FormForm

Factor Factor

FormForm

Standard Standard FormForm

25 2x2x2x2x2 32

72 7x7 49

43 4x4x4 64

104 10x10x10x10 10,000

53 5x5x5 125

Powers of tenPowers of ten

PlacePlace

ValueValueExponent Exponent

FormFormFactorFactor

FormForm

Standard Standard

FormForm

OnesOnes 101000 11

TensTens 101011 1010 1010

HundredsHundreds 101022 10x1010x10 100100

ThousandsThousands 101033 10x10x1010x10x10 10001000

Ten ThousandsTen Thousands 101044 10x10x10x1010x10x10x10 10,00010,000

Hundred Hundred ThousandsThousands 101055 10x10x10x10x1010x10x10x10x10 100,000100,000

MillionsMillions 101066 10x10x10x10x10x10x10x10x10x10x1010 1,000,0001,000,000

Exponents tell how many times a number, called a BASEBASE, is used as a factor.

77² = 7 x 7² = 7 x 7

In 6 x 6, 6 is used as a factor twice. When you compute 6 x 66 x 6 or 66²², you are finding the SQUARESQUARE of 6. of 6.

6

6

Numbers like 36, 49, 36, 49, andand 625 625 are called are called PERFECT SQUARES,PERFECT SQUARES, because they are because they are

the squares of whole numbers.the squares of whole numbers.6

6

Perfect Perfect

SquareSquare

If 66 is the number you would square to is the number you would square to find 36, then find 36, then 6 6 is the is the square root square root of of 36.36.

66² = 36² = 36

√√36 = 636 = 6

What number would you square or is the What number would you square or is the square root of 9?square root of 9?

9

33

33

A radical sign ( A radical sign ( √ ) is placed over a√ ) is placed over anumber when the number when the square rootsquare root is requested. is requested.

Construct a Construct a Square Root ChartSquare Root Chart with your with your partnerpartner showing the numbers that 1-20 showing the numbers that 1-20

are the square roots of!are the square roots of!

ExampleExampleSquare Square

RootRoot

√ √ 11 11

√ √ 44 22

√ √ 99 33

√ √ 1616 44

√ √ 2525 55

What number would you square or is the What number would you square or is the square root of the following numbers:square root of the following numbers:

1) 1) √ 81 = √ 81 =

2) √ 121 =2) √ 121 =

3) √ 49 =3) √ 49 =

4) √ 196 =4) √ 196 =

99

1111

77

1414

( 9 x 9 )( 9 x 9 )

( 11 x 11 )( 11 x 11 )

( 7 x 7 )( 7 x 7 )

( 14 x 14 )( 14 x 14 )