Objective - To simplify expressions involving exponents.

34

= 3 3 3 3 = 81

Exponent

Base

Read, “Three to the fourth power.”

Rewrite each power as repeated multiplicationand evaluate.

1)

2)

3)

4)

25

42

310

212

5 5= • 25=

2 2 2 2= • • •16=

10 10 10= • •1000=12 12= • 144=

7 units3

Addition - One-Dimensional Growth

+ =+ 4 =

Multiplication - Two-Dimensional Growth

“Three added to four”

“Three times four” or “Three groups of four”

+ + =

+4 +4 4 = 12 square units

Exponents - Multi-Dimensional Growth“Three to the third power” “Three to the fourth power”

3 33 33 3 3 3= • •

327 un=

43 3 3 3 3= • • •381 un=

3(4) =Multiplication Repeated Addition→

Exponents Repeated Multiplication→

Power Verbal Phrase Meaning27 “Seven to the 2nd power” 7 7•

“Seven squared”

35 “Five to the 3rd power” 5 5 5• •“Five cubed”

49 “Nine to the 4th power” 9 9 9 9• • •

52 “Two to the 5th power” 2 2 2 2 2• • • •

Perimeterof a Square

Area ofa Square

Volume of a Cube

5

5

5

5

P = s + s + s + sP = 4sP 4 5= •P 20 units=

5

5

2A s=2A 5=

2A 25 un=

3V s=3V 5=

3V 125 un=

OneDimensional

TwoDimensional

ThreeDimensional

“Five Squared” “Five Cubed”

5 5

5

Simplify the following if x = 4.

1)

2)

3)

2x

4x

x10

4)

5)

6)

x2

1x

2x x•

24 16=

44 256=

410 10,000=

42 16=

24 4• 64=

14 4=

Powers of Ten

Simplify.

1)

2)

3)

310

510

810

4)

5)

6)

37 10×

81.7 10×

58 10×

10 10 10• • 1000=

100,000

100,000,000

7 1000×7000

8 100,000×800,000

1.7 100,000,000×170,000,000