Esponenziali

Index

1. Sintassi
2. Basi
3. Proprietà

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• Matematica 0 (class)

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Sintassi

$$a^b$$

• a = Base
• b = Esponente

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Basi

$$\begin{array}{rl}& 1.a^n=a_0\cdot ...\cdot a_n\to \text{Esponente intero positivo}\\ & 2.a^{-n}=\frac{1}{a^n}\to \text{Esponente intero negativo (Inverso)}\\ & 3.a^0=1\to \text{Esponente 0}\\ & 4.a^{\frac{1}{n}}=\sqrt[n]{a}\to \text{Esponente razionale }\end{array}$$

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Proprietà

$$\begin{array}{rl}& oss:(n,m)\in R\\ & \\ & 1.a^n\cdot a^m=a^{n+m}\\ & \\ & 2.a^{n^m}=a^m=a^{n\cdot m}\\ & \\ & 3.\frac{a^n}{a^m}=a^{n-m}\\ & \\ & 4.(a\pm b{)}^n=a^n\pm b^n\\ & \\ & 5.(a\cdot b{)}^n=a^n\cdot b^n\\ & \\ & 6.{\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n}\\ & \\ & 7.-sea>1\to a^n>a^{m}oss:sen>m\\ & -sea<1\to a^n<a^{m}oss:sen>m\end{array}$$

oss

$$ser\in \mathbb{Q},r=\frac{p}{q}⟹x^{\frac{p}{q}}=x^r\text{eˋ definito solo per }x\ge 0$$ $$2^x=sup\{2^r,r\in \mathbb{Q},r\le \sqrt{2}\}$$