7. Calculate $$\sqrt{0.01 x^8 y^2}$$ при $$x=3, y=7$$.

Let's solve this step-by-step:

1. We need to calculate $$\sqrt{0.01 x^8 y^2}$$.
2. We can take the square root of each factor inside the square root: $$\sqrt{0.01} \times \sqrt{x^8} \times \sqrt{y^2}$$.
3. $$\sqrt{0.01} = 0.1$$ (since $$0.1 \times 0.1 = 0.01$$).
4. $$\sqrt{x^8} = x^{8/2} = x^4$$.
5. $$\sqrt{y^2} = |y|$$.
6. So, the expression simplifies to $$0.1 x^4 |y|$$.
7. Now, substitute the given values: $$x=3$$ and $$y=7$$.
8. $$0.1 \times (3^4) \times |7|$$.
9. Calculate $$3^4$$: $$3 \times 3 \times 3 \times 3 = 9 \times 9 = 81$$.
10. Since $$y=7$$ is positive, $$|7| = 7$$.
11. So, we have $$0.1 \times 81 \times 7$$.
12. $$0.1 \times 81 = 8.1$$.
13. $$8.1 \times 7 = 56.7$$.

Ответ: 56.7