If a > 0 {\displaystyle a>0} and a ≠ 1 {\displaystyle a\neq 1} , then the exponential function with base a {\displaystyle a} is a x {\displaystyle a^{x}}
Let a {\displaystyle a} and b {\displaystyle b} be positive real numbers, and let x {\displaystyle x} and y {\displaystyle y} be real numbers.
1. a 0 = 1 {\displaystyle a^{0}=1}
2. a x a y = a x + y {\displaystyle a^{x}a^{y}=a^{x+y}}
3. a x a y = a x − y {\displaystyle {\frac {a^{x}}{a^{y}}}=a^{x-y}}
4. ( a x ) y = a x y {\displaystyle (a^{x})^{y}=a^{xy}}
5. ( a b ) x = a x b x {\displaystyle (ab)^{x}=a^{x}b^{x}}
6. ( a b ) x = a x b x {\displaystyle ({\frac {a}{b}})^{x}={\frac {a^{x}}{b^{x}}}}
7. a − x = 1 a x {\displaystyle a^{-x}={\frac {1}{a^{x}}}}
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