Machten Basisregels (xa)b=xa⋅b\Large (x^{\textcolor{blue}{a}})^{\textcolor{red}{b}} = x^{\textcolor{blue}{a}\cdot\textcolor{red}{b}}(xa)b=xa⋅b xa⋅xb=xa+b\Large x^{\textcolor{blue}{a}}\cdot x^{\textcolor{red}{b}} = x^{\textcolor{blue}{a}+\textcolor{red}{b}}xa⋅xb=xa+b xaxb=xa−b\Large \frac{x^{\textcolor{blue}{a}}}{x^{\textcolor{red}{b}}} = x^{\textcolor{blue}{a}-\textcolor{red}{b}}xbxa=xa−b Machten en vermenigvuldigen ax⋅b=b⋅ax\Large \textcolor{blue}{a}^x\cdot\textcolor{red}{b} = \textcolor{red}{b}\cdot\textcolor{blue}{a}^xax⋅b=b⋅ax a⋅bx⋅c=(a⋅c)⋅bx\Large \textcolor{blue}{a}\cdot\textcolor{red}{b}^x\cdot\textcolor{green}{c} = (\textcolor{blue}{a}\cdot \textcolor{green}{c})\cdot\textcolor{red}{b}^{x}a⋅bx⋅c=(a⋅c)⋅bx a⋅bx⋅b=a⋅bx+1\Large \textcolor{blue}{a}\cdot\textcolor{red}{b}^x\cdot\textcolor{red}{b} = \textcolor{blue}{a}\cdot\textcolor{red}{b}^{x+1}a⋅bx⋅b=a⋅bx+1 Complexe regels voor machten axn⋅bxm=(a⋅b)xn+m\Large \textcolor{blue}{a}x^{\textcolor{green}{n}}\cdot\textcolor{red}{b}x^{\textcolor{orange}{m}} = (\textcolor{blue}{a}\cdot \textcolor{red}{b})x^{\textcolor{green}{n}+\textcolor{orange}{m}}axn⋅bxm=(a⋅b)xn+m n≠m⇒axn+bxm=axn+bxm\Large \textcolor{green}{n} \neq \textcolor{orange}{m} \Rightarrow \textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{orange}{m}} = \textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{orange}{m}}n=m⇒axn+bxm=axn+bxm axn+bxn=(a+b)xn\Large \textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{green}{n}} = (\textcolor{blue}{a}+\textcolor{red}{b})x^{\textcolor{green}{n}}axn+bxn=(a+b)xn