Download 7.2 Apply Exponent Properties Involving Quotients - Welcome

Warm up
1) Evaluate
2) Evaluate
3) Evaluate
4) Evaluate
1
𝑞 𝑤ℎ𝑒𝑛 𝑞 =
4
3
2
𝑐 𝑤ℎ𝑒𝑛 𝑐 =
5
1
4
𝑑 𝑤ℎ𝑒𝑛 𝑑 =
2
3
6
𝑒 𝑤ℎ𝑒𝑛 𝑒 =
2
3
7.2 Apply Exponent Properties
Involving Quotients
• Notice what happens when you divide powers
with the same base
𝑎5 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎
2
5−3
=
=
𝑎
∙
𝑎
=
𝑎
=
𝑎
𝑎3
𝑎∙𝑎∙𝑎
Can you guess what the Rule is?
Key Concept
• Quotient of Powers Property
• Let a be a nonzero real number and let m and
n be positive integers such that 𝑚 > 𝑛
• WORDS: To divide powers having the same
base subtract the exponents
• Algebra:
𝑎𝑚
𝑎𝑛
• Example:
47
42
= 𝑎𝑚−𝑛 , 𝑎 ≠ 0
= 47−2 = 45
Example 1 Use the quotient of powers
property
a.
810
84
b.
(−3)9
(−3)3
c.
d.
54 ∙58
57
1
6
∙
𝑥
𝑥4
Power of a Quotient
• Notice what happens when you raise a
quotient to a power
•
𝑎 4 𝑎
( ) =
𝑏
𝑏
𝑎
𝑏
𝑎
𝑏
𝑎
𝑏
∙ ∙ ∙ =
𝑎∙𝑎∙𝑎∙𝑎
𝑏∙𝑏∙𝑏∙𝑏
• Can you guess the rule?
=
𝑎4
𝑏4
Key Concept
• Power of a Quotient Property
• Let a and b be real numbers with 𝑏 ≠ 0, and let
m be a positive integer
• Words To find a power of a quotient, find the
power of the numerator and the power of the
denominator and divide
•
•
𝑎 𝑚 𝑎𝑚
Algebra( ) = 𝑚
𝑏
𝑏
3 7 37
EX ( ) = 7
2
2
Example 2 Use the power of a quotient
property
a.
b.
𝑥 3
( )
𝑦
7 2
(− )
𝑥
Example 3
a.
4𝑥 2 3
( )
5𝑦
b.
𝑎2 5
( )
𝑏
Astronomy
• The luminosity (in watts) of a star is the total
amount of energy emitted from the star per
unit of time. The order magnitude of the
luminosity of the sun is 1026 𝑤𝑎𝑡𝑡𝑠. He star
Canopus is one of the brightest stars in the
sky. The order of magnitude of the luminosity
of Canopus is 1030 watts. How many times
more luminous is Canopus than the sun?