3. 4 Simplify the fraction $\frac{x^{8}+x^{6} y^{2}+x^{4} y^{4}+x^{2} y^{6}+y^{8}}{x^{4}+x^{3} y+x^{2} y^{2}+x y^{3}+y^{4}}$, and calculate the value of the fraction when $x=$ $0.01, y=0.02$.
[Solution]
$$
\begin{aligned}
\text { Original expression } & =\frac{x^{10}-y^{10}}{x^{2}-y^{2}} \div \frac{x^{5}-y^{5}}{x-y} \\
& =\frac{x^{5}+y^{5}}{x+y} \\
& =x^{4}-x^{3} y+x^{2} y^{2}-x y^{3}+y^{4}
\end{aligned}
$$

When $x=0.01, y=0.02$,
$$
\begin{aligned}
\text { Original expression } & =\frac{(0.01)^{5}+(0.02)^{5}}{0.01+0.02} \\
& =\frac{11}{100^{4}} \\
& =11 \times 10^{-8} .
\end{aligned}
$$