14. Calculate $$\sqrt{a^4 \cdot (-a)^8}$$ при $$a=10$$.

Let's solve this step-by-step:

1. We need to simplify the expression $$\sqrt{a^4 \cdot (-a)^8}$$.
2. First, simplify $$(-a)^8$$. When a negative number is raised to an even power, the result is positive. So, $$(-a)^8 = a^8$$.
3. The expression inside the square root becomes $$a^4 \cdot a^8$$.
4. When multiplying exponents with the same base, add the powers: $$a^4 \cdot a^8 = a^{4+8} = a^{12}$$.
5. So, we need to calculate $$\sqrt{a^{12}}$$.
6. The square root of $$a^{12}$$ is $$a^{12/2} = a^6$$.
7. The problem states to calculate this при $$a=10$$.
8. So, substitute $$a=10$$ into $$a^6$$: $$10^6$$.
9. $$10^6 = 1,000,000$$.

Ответ: 1,000,000