Download Quotient of Powers Quotient of Powers Property 42

Quotient of Powers
Quotient of Powers Property
Let a be a real number, and let m and n be positive integers such
than m>n.
WORDS: To divide powers having the same base, subtract the
exponents.
ALGEBRA:
am
mn

a
an
EXAMPLE:
47 = 47-2 = 45
42
Example 1: Use the quotient
of powers property
Quotient of Powers
Simplify the expression:
612
a. 5  6125
6
 67
When simplifying powers
with numerical bases only,
write your answer using
exponents.
(2)
 (2)74  (2)3
4
(2)
7
b.
42  48
c. 4 
4
410
44
= 410-4
1 12
y12
d. 9  y 
= y12-9
9
y
y
= 46
 y3
Power of a Quotient
Power of a Quotient Property
Let a and b be real numbers, 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.
m
ALGEBRA:
am
a
   m
b
b
3
EXAMPLE:
3
4 4
   3
8 7
Example 2: Use the power of
a quotient property
Power of a Quotient
Simplify:
5
r
a.   
s
æ 4ö
b.ç - ÷ =
è wø
3
r5
s5
4)
(
w
3
3
=
-
64
w3
When simplifying powers
with numerical and variable
bases, evaluate the numerical
power.
Checkpoint
Simplify the expression.
1)
(– 8)8
8 – 5 = (– 8)3
=
(–
8)
(– 8)5
2) - r
3
3)
2
r
=- 2
3
2
35 34 = 39
33
33
= 39 – 3
= 36
r2
=9
4)
5
t
4
54
= 4
t
=
625
t4
EXAMPLE 3
2y7
y5
Use properties of exponents
3
(2y7)3
=
(y 5 )3
23 (y7)3
=
(y5 )3
8y21
= 15
y
=
8y6
Power of a quotient property
Power of a product property
Power of a power property
Quotient of a power property
Checkpoint
Simplify the expressions.
Work on the checkpoint problems…I will take volunteers
to put them on the back board…
EXAMPLE 4
Order of Magnitude
The order of magnitude of a quantity is the power of 10 closest to that quantity.
Distances
The distance from Earth to the nearest galaxy is
about 10 22meters. The distance from Earth to the
North Star is about 1019meters. How many times
further from Earth is the nearest galaxy than the
North Star?
Distance to Galaxy
1022
1019
Distance to North Star
3
=
103
The nearest galaxy is 10 times further than the
North Star.
Checkpoint
9. The distance from the sun to Saturn is 1012 meters. The
distance from the sun to Venus is 1011 meters. How much
further is Saturn than Venus from the sun?
SOLUTION
10 times further
Checkpoint
10. The GDP (Gross Domestic Product) of the U.S. is
approximately 10,753,000,000 dollars and the GDP
of an underdeveloped country 9,872 dollars. Use order
of magnitude to estimate how many times greater the
United State’s GDP is compared to an underdeveloped
Country.
SOLUTION
10,753,000,000
Order of magnitude = 1010
9,872
Order of magnitude = 104
United State’s GDP is 106 times greater.