Exponents Formulas

1. If p is positive integer, and a \in \mathbb{R}, then {a^p} = a \cdot a \cdot a \cdots to p factors.

2. \forall a \in \mathbb{R},        a \ne 0, {a^0}  = 1

3. {a^r} \cdot {a^s} = {a^{r + s}},         a \in  \mathbb{R}; r,s \in \mathbb{N};a \ne  0

4. {({a^r})^s} = {a^{rs}}

5. {(ab)^r} = {a^r} \cdot {b^r}         a \in  \mathbb{R}; r \in \mathbb{N};a,b \ne  0

6. {1^n} = 1         \forall  n \in \mathbb{N}

7. \frac{{{a^r}}}{{{a^s}}} = {a^{r - s}},        a \in \mathbb{R}; r,s \in \mathbb{N};a \ne 0

8. {(\frac{a}{b})^r} = \frac{{{a^r}}}{{{b^r}}}         a  \in \mathbb{R}; r \in \mathbb{N};a,b  \ne 0

9. {a^{ - r}} = \frac{1}{{{a^r}}}         a  \in \mathbb{R}; r \in \mathbb{N};a  \ne 0

10. {a^{\frac{r}{s}}} = \sqrt[s]{{{a^r}}}         a \in \mathbb{R}; r,s \in \mathbb{N};a \ne 0