$$\frac{25\times5^{2}\times t^{8}}{10^{3}\times t^{4}}$$
$\frac{5t^{4}}{8}$
$$\frac{25\times 5^{2}t^{4}}{10^{3}}$$
$$\frac{25\times 25t^{4}}{10^{3}}$$
$$\frac{625t^{4}}{10^{3}}$$
$$\frac{625t^{4}}{1000}$$
$$\frac{5}{8}t^{4}$$
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$\frac{5t^{3}}{2}$
$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{25\times 5^{2}t^{4}}{10^{3}})$$
$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{25\times 25t^{4}}{10^{3}})$$
$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{625t^{4}}{10^{3}})$$
$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{625t^{4}}{1000})$$
$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{5}{8}t^{4})$$
$$4\times \frac{5}{8}t^{4-1}$$
$$\frac{5}{2}t^{4-1}$$
$$\frac{5}{2}t^{3}$$
