1. The problem is to simplify the expression $$\frac{a^2 \cdot a^5 \cdot a^6}{a^8} = 8$$ and solve for $a$. 2. Recall the rule for multiplying powers with the same base: $$a^m \cdot a^n = a^{m+n}$$ and for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. Apply the multiplication rule to the numerator: $$a^2 \cdot a^5 \cdot a^6 = a^{2+5+6} = a^{13}$$. 4. Now rewrite the expression: $$\frac{a^{13}}{a^8} = a^{13-8} = a^5$$. 5. The equation becomes: $$a^5 = 8$$. 6. To solve for $a$, take the fifth root of both sides: $$a = \sqrt[5]{8}$$. 7. Since $8 = 2^3$, $$a = \sqrt[5]{2^3} = 2^{\frac{3}{5}}$$. 8. Therefore, the solution is $$a = 2^{\frac{3}{5}}$$.