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Here are a few recommended readings before getting started with this lesson.
Here are a few practice exercises before getting started with this lesson.
The following table shows the Properties of Exponents.
Product of Powers Property | aman=am+n |
---|---|
Quotient of Powers Property | anam=am−n |
Power of a Product Property | (ab)n=anbn |
Power of a Quotient Property | (ba)n=bnan |
Power of a Power Property | (am)n=am⋅n |
(am)n=am⋅n
nam=anm
Write as a product of fractions
rp=m, rq=n
anm=nam
Start by using the Commutative Property of Multiplication.
\CommutativePropMult
am⋅an=am+n
ba=b⋅3a⋅3
ba=b⋅2a⋅2
Add fractions
Multiply
anm=nam
Start by using the Commutative Property of Multiplication. Then, use the Product of Powers Property for Rational Exponents. Finally, apply the Quotient of Powers Property for Rational Exponents.
\CommutativePropMult
am⋅an=am+n
ba=b⋅11a⋅11
ba=b⋅3a⋅3
Add fractions
Write as a product of fractions
anam=am−n
ba=b⋅3a⋅3
ba=b⋅9a⋅9
ba=b⋅2a⋅2
Subtract fractions
Multiply
Use and combine the properties of exponents presented in this lesson.
The properties of rational exponents can be combined to simplify algebraic or numeric expressions. Analyze each of the given expressions one at a time.
ca⋅b=ca⋅b
anam=am−n
a=a21
\CommutativePropMult
a=a1
am⋅an=am+n
ca⋅b=ca⋅b
\CommutativePropMult
am⋅an=am+n
Add fractions
Write as a product of fractions
ca⋅b=ca⋅b
Below are the formulas for the surface area and the volume of a sphere with radius r.
a=a21
(ba)m=bmam
(ab)m=ambm
a21=a
Calculate root
Rearrange equation
r=2π21SA21
(ba)m=bmam
(ab)m=ambm
Calculate power
(am)n=am⋅n
b1⋅a=ba
Multiply fractions
ba=b/4a/4
\CommutativePropMult
Write as a product of fractions
a=a1
anam=am−n
a-m=am1
Multiply fractions
a=a21
na=an1
(ab)m=ambm
Rewrite 8 as 23
(am)n=am⋅n
\CommutativePropMult
am⋅an=am+n
Write as a product of fractions
anam=am−n
Subtract terms
ba=b⋅3a⋅3
ba=b⋅2a⋅2
a=33⋅a
Subtract fractions