8.2
TRANSCRIPT
Quotient of Powers Property
To divide powers having the same base, subtract exponents.
0, aaa
a nmn
m
Example 1 Use the quotient of powers property
a.
86=
84
810
= 810 – 4
( )11 – 45–=
( )75–=
=( )115–( )45–
b.( )45–
1( )115–•
Power of a Quotient Property
To find a power of a quotient, find the power of the numerator and the power of the denominator and divide.
Example 2 Use the power of a quotient property
Simplify the expression.
a. 6
5 2
b. 3
2 3–
Power of a quotient property
SOLUTION
a. 6
5 2
=62
52
Place negative sign in numerator.b. 3
2 3– =
3
2 3–
=33
2 3–( )Power of a quotient property
Summary of Exponent Properties
Quotient of Power:
Power of a Quotient:
0, aaa
a nmn
m
Example 3 Use the quotient of powers property
b.x2
x3y=x2
x3
1
y•
x3 – 2 • y=
xy=
a.x3
x7
= x7 – 3
x4=
Example 4 Use the power of a quotient property
Simplify the expression.
a. yx 5
b. x
7 2–
=x2
7 2–( )Power of a quotient property
b.
Place negative sign in numerator.=x
7 2–x
7 2–
Power of a quotient property=y5
x5
a.
SOLUTION
yx 5
Example 4 Use the power of a quotient property
=x2
49Simplify.
Example 5 Use properties of exponents
a. 5y
4x2 3
=5y
4x2 3( )
( )3Power of a quotient property
=53y3
x2 3( )43 •Power of a product property
=125y3
64x6
Power of a power property
b.
b
a2 5
2a2
1• Power of a quotient property=
( )a2 5
b5 2a2
1•
Example 5 Use properties of exponents
Power of a power property=2a2
1•
b5
a10
Multiply fractions.=2a2 b5
a10
Quotient of powers property=2b5
a8
8.2 Warm-up (Day 1)Simplify the expression. Write your answer using
exponents.
1) 2)
3) 4)
5)
8.2 Warm-up (Day 2)Simplify the expression. Write your answer using
exponents.
1) 2)
3) 4)
5)