#### Answer

$t=0$ or $t=\displaystyle \frac{\sqrt[3]{2}}{5}$

#### Work Step by Step

We solve by factoring:
$125t^{10}-2t^{7}=0$
$t^{7}(125t^{3}-2)=0$
$t^7=0$ or $125t^{3}-2=0$
$t=0$ or $t^3=2/125$
$t=0$ or $t=\displaystyle \sqrt[3]{\frac{2}{125}}=\frac{\sqrt[3]{2}}{5}$