a ∈ R ve n ∈ Z⁺ olmak üzere ;
https://www.matematiktutkusu.com/for...e/matadszi.jpg (a: taban, n: üs)


1) a ≠ 0 için a⁰=1 dir. (0⁰ belirsizdir.)

a¹=a, a²=a.a (a kare), a³=a.a.a (a küp)



2) a > 0 için (-a)²ⁿ=a²ⁿ > 0 dır.

Örnek ---> [(-3)²=(3)² =9 > 0]




3) a > 0 için (-a)^2n-1=-a^2n-1 < 0 dır.

Örnek ---> [(-4)³=-4³=-64 < 0]




4) (a-b)²ⁿ=(b-a)²ⁿ, (a-b)^2n-1=-(b-a)^2n-1




5) aⁿ=a^m ise n=m dir. (a ≠ 0, a ≠ 1, a ≠ -1)

Örnek ---> (2^x=8 ise 2^x=2³, x=3)




6) axⁿ+bxⁿ+cx^m-dx^m+ex^m=(a+b)xⁿ+(c-d+e)x^m

Örnek ---> [2.2¹⁰+5.2¹⁰-3.2¹⁰=(2+5-3).2¹⁰=4.2¹⁰


7) a^m.aⁿ=a^m+n, (a⁴.a³=a⁷) <--> a^m.b^m=(a.b)^m, (a⁵.b⁵)=(a.b)⁵


8)

https://chart.apis.google.com/chart?...-n%5Cright)%7D
https://chart.apis.google.com/chart?...%3Da%5E%7B4%7D

https://chart.apis.google.com/chart?...ght)%5E%7Bm%7D (b ≠ 0)
https://chart.apis.google.com/chart?...ght)%5E%7B5%7D

9)
https://chart.apis.google.com/chart?...E%7Bm%7D%7D%20 ; https://chart.apis.google.com/chart?...E%7B5%7D%7D%20 ; https://chart.apis.google.com/chart?...ght)%5E%7Bm%7D ;

https://chart.apis.google.com/chart?...6%7D%7B9%7D%20 ; https://chart.apis.google.com/chart?...E%7Bm%7D%7D%20 ;

https://chart.apis.google.com/chart?...%7D%7B16%7D%20 , https://chart.apis.google.com/chart?...1%7D%7B8%7D%20 , https://chart.apis.google.com/chart?...%7D%7B16%7D%20



10) (a^m)ⁿ=a^m.n (a⁴)³=a¹²