1. **State the problem:** Simplify the expression $$\frac{(-2)^3 \times (-2)^4}{(-2)^2 \times (-2)^5} + \frac{(-1)^0 \times (-1)^3}{(-1)^4 \times (-1)^x} \cdot \frac{(-1)^3 \cdot (-2) \cdot (-2)^2 + (-1)^9}{(-1)^{14} - 1 \cdot (-1)^3} \div \frac{(-1)^{14} \cdot (-1)^1}{1 \div (-1)^{10} \cdot (-1)^1}.$ 2. **Use exponent rules:** - $a^m \times a^n = a^{m+n}$ - $\frac{a^m}{a^n} = a^{m-n}$ - $a^0 = 1$ - $(-1)^n = -1$ if $n$ is odd, $1$ if $n$ is even 3. **Simplify numerator and denominator of first fraction:** $$(-2)^3 \times (-2)^4 = (-2)^{3+4} = (-2)^7$$ $$(-2)^2 \times (-2)^5 = (-2)^{2+5} = (-2)^7$$ 4. **Simplify first fraction:** $$\frac{(-2)^7}{(-2)^7} = (-2)^{7-7} = (-2)^0 = 1$$ 5. **Simplify second fraction numerator:** $$(-1)^0 \times (-1)^3 = 1 \times (-1)^3 = (-1)^3 = -1$$ 6. **Simplify second fraction denominator:** $$(-1)^4 \times (-1)^x = (-1)^{4+x} = 1 \times (-1)^x = (-1)^x$$ 7. **Second fraction becomes:** $$\frac{-1}{(-1)^x} = -1 \times (-1)^{-x} = -(-1)^x$$ 8. **Simplify inside the big numerator of the complex fraction:** $$(-1)^3 \cdot (-2) \cdot (-2)^2 = (-1)^3 \cdot (-2)^{1+2} = (-1)^3 \cdot (-2)^3 = (-1)^3 \cdot (-8) = -1 \times -8 = 8$$ 9. **Add $(-1)^9$ to above:** $$8 + (-1)^9 = 8 + (-1) = 7$$ 10. **Simplify denominator of complex fraction:** $$(-1)^{14} - 1 \cdot (-1)^3 = 1 - (-1) = 1 + 1 = 2$$ 11. **Complex fraction becomes:** $$\frac{7}{2}$$ 12. **Simplify division by fraction:** $$\div \frac{(-1)^{14} \cdot (-1)^1}{1 \div (-1)^{10} \cdot (-1)^1} = \times \frac{1 \div (-1)^{10} \cdot (-1)^1}{(-1)^{14} \cdot (-1)^1}$$ 13. **Simplify powers:** $$(-1)^{14} = 1, \quad (-1)^{10} = 1$$ 14. **Simplify numerator of division:** $$1 \div 1 \times (-1)^1 = 1 \times (-1) = -1$$ 15. **Simplify denominator of division:** $$1 \times (-1)^1 = -1$$ 16. **Division fraction becomes:** $$\frac{-1}{-1} = 1$$ 17. **Multiply all parts:** $$1 + (-(-1)^x) \times \frac{7}{2} \times 1 = 1 - (-1)^x \times \frac{7}{2}$$ 18. **Final simplified expression:** $$1 - \frac{7}{2} (-1)^x$$ **Answer:** $$\boxed{1 - \frac{7}{2} (-1)^x}$$