Integer Exponents

Powers

a a a an

n

factors

If a is a real number and n is a positive integer,

a a0 1 0 if

aa

ann

10 if

4 4 4 43

6 10

41

43

3

Laws of Exponents

a a a a a ab a b

a

aa

aa

ab

a

bb

m n m n m n mn n n n

m

nm n

n m

n n

n

if

if

10

0

ab

ba

a bn n

if 0 0,

Write so that all exponents are positive.x y

x y

3 2

1 4

x y

x y

x

x

y

y

3 2

1 4

3

1

2

4

x y3 1 2 4( )

x y4 6 xy

4

6

3 2 4

3

2x y

x y

Simplify each expression. Express the answer so only positive exponents occur.

3 2 3 4 1 2x y

3 1 3 2x y

3 2 1 2 3 2

x y 3 2 2 6x y x

y

2

69

From Decimal to Scientific Notation

1. Count the number N of places that the decimal point must be moved in order to arrive at a number x, where 1 < x < 10.

2. If the original number is greater than or equal to 1, the scientific notation is If the original number is between 0 and 1, the scientific notation is

x N10 .

x N 10 .

Write the number 5,100,000,000 in scientific notation.

51 109.

Write the number 0.00032 in scientific notation.

3 2 10 4.

Write as a decimal.4 3 10 5.

0.000043