Multiplikation:
a n ⋅ a m = a n + m {\displaystyle a^{n}\cdot a^{m}=a^{n+m}}
4 3 ⋅ 4 6 = 4 3 + 6 = 4 9 a t ⋅ a q = a t + q x 3 ⋅ x 57 = x 3 + 57 = x 60 {\displaystyle 4^{3}\cdot 4^{6}=4^{3+6}=4^{9}\quad \quad a^{t}\cdot a^{q}=a^{t+q}\quad \quad x^{3}\cdot x^{57}=x^{3+57}=x^{60}}
4 7 ⋅ 4 − 2 = 4 7 + ( − 2 ) = 4 5 a t ⋅ a − q = a t + ( − q ) = a t − q x 3 ⋅ x − 7 = x 3 + ( − 7 ) = x 3 − 7 = x − 4 {\displaystyle 4^{7}\cdot 4^{-2}=4^{7+(-2)}=4^{5}\quad \quad a^{t}\cdot a^{-q}=a^{t+(-q)}=a^{t-q}\quad \quad x^{3}\cdot x^{-7}=x^{3+(-7)}=x^{3-7}=x^{-4}}
Division:
a n a m = a n − m {\displaystyle {\frac {a^{n}}{a^{m}}}=a^{n-m}}
a 7 a 5 = a 7 − 5 = 7 2 7 74 7 5 = 7 74 − 5 = 7 69 4 z 4 x = 4 z − x {\displaystyle {\frac {a^{7}}{a^{5}}}=a^{7-5}=7^{2}\quad \quad {\frac {7^{74}}{7^{5}}}=7^{74-5}=7^{69}\quad \quad {\frac {4^{z}}{4^{x}}}=4^{z-x}}
w 5 w − 7 = w 5 : w − 7 = w 5 − ( − 7 ) = w 5 + 7 = w 12 {\displaystyle {\frac {w^{5}}{w^{-7}}}=w^{5}:w^{-7}=w^{5-(-7)}=w^{5+7}=w^{12}}
a − 7 a 5 = a − 7 : a 5 = a − 7 − 5 = a − 12 {\displaystyle {\frac {a^{-7}}{a^{5}}}=a^{-7}:a^{5}=a^{-7-5}=a^{-12}}
4 − 7 4 − c = 4 − 7 : 4 − c = 4 − 7 − ( − c ) = 4 − 7 + c {\displaystyle {\frac {4^{-7}}{4^{-c}}}=4^{-7}:4^{-c}=4^{-7-(-c)}=4^{-7+c}}
