Exponential Formulas

 

\( a^p = \underbrace{a \cdot a \cdot \dots a }_p ~~~( \text{if} ~~ p \in \mathbb{N} ) \)

 

\( a^0 = 1 ~~~ (\text{if} ~~~ a \ne 0) \)

 

\( a^r \cdot a^s = a^{r+s} \)

 

\( \frac{a^r}{a^s} = a^{r-s} \)

 

\( \left( a^r\right)^s = a^{r \cdot s} \)

 

\( (a \cdot b)^r = a^r \cdot b^r \)

 

\( \left( \frac{a}{b} \right)^r = \frac{a^r}{b^r} \)

 

\( a^{-r} = \frac{1}{a^r} \)

 

\( a^{\Large\frac{r}{s}} = \sqrt[\Large{s}]{a^r} \)

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