**1.5.1. Exponential functions**

**Exponential function:** \(f(x)=a^x\) where \(a>0\). **Power function: **\(g(x) = x^a\) **Natural exponential function: **\(\exp(x)=e^x\)

\(a^nb^n = a^{n+m}\), \(\frac{a^n}{a^m} = a^{n-m}\), \(\frac{a^n}{b^n} = \left(\frac{a}{b}\right)^{n}\),

\(a^nb^n = (ab)^n\), \((a^n)^m = a^{nm}\), \(a^0=1\), \(a^1=a\), \(a^{-n}= \frac{1}{a^n}\)