using properties of exponents. properties of exponents a&b are real numbers, m&n are...
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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 ≈≈