6. Calculate $$\sqrt{\frac{64a^{20}}{a^{18}}}$$ при $$a=5$$.

Let's solve this step-by-step:

1. Simplify the expression inside the square root first: $$\frac{64a^{20}}{a^{18}}$$.
2. When dividing exponents with the same base, subtract the powers: $$a^{20} \div a^{18} = a^{20-18} = a^2$$.
3. So, the expression inside the square root becomes $$64a^2$$.
4. Now, we need to calculate $$\sqrt{64a^2}$$.
5. We can take the square root of the coefficient and the variable separately: $$\sqrt{64} \times \sqrt{a^2}$$.
6. $$\sqrt{64} = 8$$.
7. $$\sqrt{a^2} = |a|$$. Since $$a$$ is squared, the result is always non-negative.
8. So, $$\sqrt{64a^2} = 8|a|$$.
9. The problem states to calculate this при $$a=5$$. Since 5 is positive, $$|a|$$ is just $$a$$.
10. So, we have $$8 \times 5$$.
11. $$8 \times 5 = 40$$.

Ответ: 40