How do you simplify ((4t^3)(2t))/(20t^2) and what are the excluded values for the variable?

Apr 12, 2017

$\frac{\left(4 {t}^{3}\right) \left(2 t\right)}{20 {t}^{2}} = \textcolor{g r e e n}{\frac{2}{5} {t}^{2}}$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXXX}} \textcolor{red}{t \ne 0}$

Explanation:

$\textcolor{red}{t = 0}$ must be excluded since this would result in an undefined expression value: $\frac{0}{0}$

$\frac{\left(4 {t}^{3}\right) \left(2 t\right)}{20 {t}^{2}}$
$\textcolor{w h i t e}{\text{XXX}} = \frac{\left(\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{4}}} \textcolor{m a \ge n t a}{{\cancel{\textcolor{b l a c k}{{t}^{3}}}}^{t}}\right) \left(2 t\right)}{\textcolor{b l u e}{{\cancel{\textcolor{b l a c k}{20}}}_{5}} \textcolor{m a \ge n t a}{\cancel{\textcolor{b l a c k}{{t}^{2}}}}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{2 {t}^{2}}{5}$