Using Properties of Exponents

Properties of Exponentsa&b are real numbers, m&n are integers

• Product Property: am * an=am+n

• Power of a Power Property: (am)n=amn

• Power of a Product Property: (ab)m=ambm

• Negative Exponent Property: a-m= ; a≠0• Zero Exponent Property: a0=1; a≠0• Quotient of Powers: am = am-n; a≠0

an

• Power of Quotient: b≠0m

mm

b

a

b

a=⎟

⎠

⎞⎜⎝

⎛

ma

1

Example 1 – Product Property

• (-5)4 * (-5)5 =

• (-5)4+5 =

• (-5)9 =

• -1953125

Example 2

• x5 * x2 =

• x5+2 =

• x7

Example 3 – Power of a Power

• (23)4 =

• 23*4 =

• 212 =

• 4096

Example 4

• (34)2 =

• 34*2 =

• 38 =

• 6561

Example 5 – Neg. Exponent

• (-5)-6(-5)4 =

• (-5)-6+4 =

• (-5)-2 =

( )=

− 25

1

25

1

Example 6 – Quotient of Powers

=3

5

x

x =−35x 2x

Example 7 – Power of Quotient

=⎟⎠

⎞⎜⎝

⎛−

2

5s

r

( ) =− 25

2

s

r =−10

2

s

r 102sr

Example 8 – Zero Exponent

• (7b-3)2 b5 b = • 72 b-3*2 b5 b = • 49 b-6+5+1 = • 49b0 =• 49

Example 9 – Quotient of Powers

=10

5

x

x =−105x =−5x 5

1

x

Scientific Notation

• 131,400,000,000=

1.314 x 1011

Move the decimal behind the 1st number

How many places did you have to move the decimal?

Put that number here!

Example – Scientific Notation

• 131,400,000,000 =• 5,284,000

1.314 x 1011 =

5.284 x 106

61110*284.5

314.1 − 900,2410*249. 5 ≈≈