Section P2Exponents and Scientific Notation

The Product Rule

Example

3 5 25 4x y x y

Simplify:

5 37 9x x

The Quotient Rule

Example

7

3

22

Simplify:

48 32x yx

Example

5 3 2

2

4816x y zx y

Simplify:

Zero as an Exponent

Example

5 0

5

66z

7 7x x

Simplify:

The Negative-Exponent Rule

Example

2( 5)

2 43x y

Simplify Exponential Expressions

25

Example

44

2

17

Simplify Exponential Expressions

The Power Rule for Exponents (Powers to Powers)

Example

45

22

54

3

b

y

Simplify Exponential Expressions

Power of a Product

Example

343x

236x y

Simplify Exponential Expressions

Power of a Quotient

Example

32

3

5xy

24

3

xy

Simplify Exponential Expressions

Simplifying Exponential Expressions

Example

3 4

2 8 3 8

3 7

5 4

27

2

( 2 )

7 2

42

546

x y

x y x y

x yx y

yzz

Simplify Exponential Expressions

Use Scientific Notation

nIn a × 10 change a number in scientific notationto decimal notation by moving the decimal point in a to the right if n is positive, and move the decimal point to the left if n is negative, n number of places.

Converting from Scientific to Decimal Notation

Example Convert from Scientific Notation to decimal notation.

5

4

2

8.3 10

2.09 10

4.045 10

Example Convert from decimal notation to scientific notation.

56,000,0004,090,000

0.00000670.00000.36

Example

6 8

7

3

7.3 10 8.0 10

4.8 103.0 10

Perform the indicated operations and write your answer in scientific notation.

Example

In 2008, Congress proposed a 700 billion dollar bailout (7 x 1011) of the US banking system. If there are 300 million people in the US, what will be the cost per person in tax dollars if every person paid an equal amount of this bailout cost?

Simplify the exponential expression

(a)

(b)

(c)

(d)

323xy

3 6

3 6

6

3 6

27

27

9

9

x y

x y

xy

x y

Simplify the exponential expression

(a)

(b)

(c)

(d)

25 3

2 4

3015

x yx y

6 14

6 7

6 14

3 7

4

4

4

2

x y

x y

x y

x y

Perform the indicated operation and write your answer in scientific notation.

(a)

(b)

(c)

(d)

4,640,000,000232,000

3

14

4

45

.2 10

2 10

2 10

2 10