10. Calculate $$\sqrt{\frac{25x^7}{y^{13}}}$$ при $$x=8, y=2$$.

Let's solve this step-by-step:

1. We need to calculate $$\sqrt{\frac{25x^7}{y^{13}}}$$.
2. We can take the square root of the numerator and the denominator separately: $$\frac{\sqrt{25x^7}}{\sqrt{y^{13}}}$$.
3. Calculate the square root of the numerator: $$\sqrt{25x^7} = \sqrt{25} \times \sqrt{x^7} = 5 \times x^{7/2}$$.
4. Calculate the square root of the denominator: $$\sqrt{y^{13}} = y^{13/2}$$.
5. So, the expression becomes $$\frac{5x^{7/2}}{y^{13/2}}$$.
6. Now, substitute the given values $$x=8$$ and $$y=2$$.
7. $$x = 8 = 2^3$$.
8. $$y = 2$$.
9. Substitute these into the expression: $$\frac{5(2^3)^{7/2}}{(2)^{13/2}}$$.
10. Simplify the exponents: $$(2^3)^{7/2} = 2^{3 \times 7/2} = 2^{21/2}$$.
11. The expression is now $$\frac{5 \cdot 2^{21/2}}{2^{13/2}}$$.
12. When dividing exponents with the same base, subtract the powers: $$2^{21/2} \div 2^{13/2} = 2^{(21/2 - 13/2)} = 2^{8/2} = 2^4$$.
13. $$2^4 = 16$$.
14. So, we have $$5 \times 16$$.
15. $$5 \times 16 = 80$$.

Ответ: 80