Elementare Algebra - Aklimex.de

Addieren a m ±a n =a m ±a n
Subtrahieren
Multiplizieren a m ⋅a n =a mn
Dividieren für m > n
Dividieren für m < n
a m
a −n=amn
a m ⋅a −n =a m−n
a m
=am−n
n
a
a m
1
= n
a a
Potenzieren a m n =a mn =a n m
Radizieren
a −m −n =a mn
n
a m = n a m
m
=a
Vorzeichen ±a 2n =a 2n
Potenzen
a m ±b m =a m ±b m
a m ⋅b m =a⋅b m
a −m ⋅b −m =a⋅b −m
n−m a−m
n =a m
1
n
b
−m= b
a m m
a
b m= b
m
a
[a m n ] p =a mnp
a m a m =2 a m
2 a m −a m =a m
a m ⋅a m =a 2m
a m ⋅a −m =a 0 =1
am
a −m=a2m
a m −n =a m−n =a −mn
±a 2n1 =±a 2n1
Achtung: −4 2 = −4⋅−4 = 4 2 = 16 aber: −4 2 = −4 2 = −16
Null und negative Exponenten
a 0 =1
a −1 = 1
a a −2 = 1
a 2
a −m ⋅a −n = 1
= a−mn
mn
a
Gebrochene Exponenten
Sonderfälle
m
p
a
n
p
a
m
n n
a = a m = n a m
−m
n 1
a = n
a m
m−n
p p
= a = a m−n
a −n = 1
a n
1
n n
a = a
a 1
n
n = a 1
n ⋅n
= a 1 = a
a
1
n
1
n
b
= a
1
n n
= b
1 n = 1 −1 2 = 1 −1 3 = −1
a
b =
n
a
n
b
a m
a m=a0 =1
1
a −n=an