All Maths Formulas

Algebra

a p = a \cdot a \cdot \dots a            p (if p \in N)

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

a 0 = 1 (if a \neq 0)

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

a r \cdot a s = a r + s

$a^r \cdot a^s = a^{r+s}$

a r a s = a r - s

$\frac{a^r}{a^s} = a^{r-s}$

(a r) s = a r \cdot s

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

(a \cdot b) r = a r \cdot b r

$(a \cdot b)^r = a^r \cdot b^r$

(a b) r = a r b r

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

a - r = 1 a r

$a^{-r} = \frac{1}{a^r}$

a r s = a r - - \sqrt s

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

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