# How do you write b^- (4/7) in radical form?

Aug 28, 2017

b^(-(4/7))=color(red)(1/(root(7)(b^4))

#### Explanation:

General observations on exponents:
$\textcolor{w h i t e}{\text{XXX}} {p}^{- q} = \frac{1}{{p}^{q}}$

$\textcolor{w h i t e}{\text{XXX}} {p}^{\frac{r}{s}} = {\left({p}^{r}\right)}^{\frac{1}{s}} = \sqrt[s]{{p}^{r}}$

Base on the above, we have
$\textcolor{w h i t e}{\text{XXX}} b \left(- \frac{4}{7}\right) = \frac{1}{{b}^{\frac{4}{7}}} = \frac{1}{\sqrt[7]{{b}^{4}}}$