Home
Random
Log in
Settings
Donations
About Wikibooks
Disclaimers
Search
Arithmetic Course/Number Operation/Power
Language
Watch
Edit
<
Arithmetic Course
|
Number Operation
Power
edit
"Power" is the number of times a number is multiplied by itself
a
n
=
a
×
⋯
×
a
⏟
n
,
{\displaystyle a^{n}=\underbrace {a\times \cdots \times a} _{n},}
a is raised to power of n is equal to a times a times a n times
Rules
edit
a
0
=
1
{\displaystyle a^{0}=1}
a
1
=
a
{\displaystyle a^{1}=a}
a
−
1
=
1
a
{\displaystyle a^{-}1={\frac {1}{a}}}
(
−
a
)
−
1
=
a
n
{\displaystyle (-a)^{-}1=a^{n}}
. n=2m
(
−
a
)
−
1
=
−
a
n
{\displaystyle (-a)^{-}1=-a^{n}}
. n=(2m+1)
Identities
edit
a
n
+
a
m
=
a
n
(
1
+
a
(
m
−
n
)
)
{\displaystyle a^{n}+a^{m}=a^{n}(1+a^{(}m-n))}
a
n
−
a
m
=
a
n
(
1
−
a
(
m
−
n
)
)
{\displaystyle a^{n}-a^{m}=a^{n}(1-a^{(}m-n))}
a
n
×
a
m
=
a
(
n
+
m
)
{\displaystyle a^{n}\times a^{m}=a^{(}n+m)}
a
n
a
m
=
a
(
n
−
m
)
{\displaystyle {\frac {a^{n}}{a^{m}}}=a^{(}n-m)}
(
a
n
)
m
=
a
(
n
m
)
{\displaystyle (a^{n})^{m}=a^{(}nm)}
(
a
b
)
n
=
a
n
a
m
{\displaystyle ({\frac {a}{b}})^{n}={\frac {a^{n}}{a^{m}}}}
