11. Calculate $$\sqrt{16x^2y^6}$$ при $$x=10, y=4$$.

Let's solve this step-by-step:

1. We need to calculate $$\sqrt{16x^2y^6}$$.
2. We can take the square root of each factor inside the square root: $$\sqrt{16} \times \sqrt{x^2} \times \sqrt{y^6}$$.
3. $$\sqrt{16} = 4$$.
4. $$\sqrt{x^2} = |x|$$.
5. $$\sqrt{y^6} = y^{6/2} = y^3$$.
6. So, the expression simplifies to $$4|x|y^3$$.
7. Now, substitute the given values: $$x=10$$ and $$y=4$$.
8. Since $$x=10$$ is positive, $$|x| = 10$$.
9. So, we have $$4 \times 10 \times 4^3$$.
10. Calculate $$4^3$$: $$4 \times 4 \times 4 = 16 \times 4 = 64$$.
11. Now, multiply all the results together: $$4 \times 10 \times 64$$.
12. $$4 \times 10 = 40$$.
13. $$40 \times 64$$.
14. $$40 \times 64 = 2560$$.

Ответ: 2560