Mathematik anwenden HAK/HUM Formelsammlung

Potenzen 5 3 Potenzen a * R ; a ≠ 0; n * N ; n > 0 a n = a·a·…·a 1222222232222225 n Faktoren a 0 = 1 a 1 = a a ‒1 = ​  1 _ a ​ a ‒n = ​  1 _  ​a​ n ​ ​= ​ 2  ​  1 _  a ​ 3 ​ n ​ Binomische Formeln a, b * R (a + b) 2 = a 2 + 2ab + b 2 (a + b) 3 = a 3 + 3a 2  b + 3ab 2 + b 3 (a – b) 2 = a 2 – 2ab + b 2 (a – b) 3 = a 3 – 3a 2  b + 3ab 2 – b 3 (a – b)(a + b) = a 2 – b 2 (a – b)(a 2 + ab + b 2 ) = a 3 – b 3 Wurzeln (Potenzen mit rationalen Exponenten) a, b * R ; a, b > 0; m, n, k * N ; m, n, k > 0 a = ​ n 9 _ b​ É a n = b ​ 9 _ a​= ​ 2 9 _ a​= ​a​ ​  1 _ 2 ​ ​ ​ n 9 _ a​= ​a​ ​  1 _ n ​ ​ ​ n 9 __ ​a​ k ​ ​= (​ n 9 _ a​)​ k ​= ​a​ ​  k _ n ​ ​ ​ n 9 ___ a·b​= ​ n 9 _ a​·​ n 9 _ b​ ​ n 9 __ ​ m 9 a​​= ​ n·m 9 _ a​ ​ n 9 _ ​  a _ b ​ ​= ​  ​ n 9 _ a​ _ ​ n 9 _ b​ ​ ​ n 9 __ ​a​ k ​ ​= ​ n·m 9 ___ ​a​ k·m ​​ Rechenregeln a, b * R ; a, b ≠ 0; r, s * Q a r ·a s = a r + s (a·b) r = a r ·b r (a r ) s = a r·s = (a s ) r a r : a s = ​  ​a​ r ​ _ ​a​ s ​ ​= a r – s ​ 2  ​  a _ b ​  3 ​ r ​= ​  ​a​ r ​ _ ​b​ r ​ ​ ​a​ n ​ ​Basis​ Exponent ​ Nur zu Prüfzwecken – Eigentum des Verlags öbv