1. **State the problem:** Simplify the expression $$\frac{(-2)^4 - 4 + 9x - 2 + 6}{2 - (-3)(2 - 5)}$$ 2. **Calculate the numerator:** Calculate $(-2)^4$ first: $$(-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16$$ Now substitute and simplify the numerator: $$16 - 4 + 9x - 2 + 6$$ Combine like terms (constants): $$16 - 4 = 12$$ $$12 - 2 = 10$$ $$10 + 6 = 16$$ So numerator becomes: $$16 + 9x$$ 3. **Calculate the denominator:** Simplify inside the parentheses: $$2 - 5 = -3$$ Multiply: $$-3 \times (-3) = 9$$ Now substitute back: $$2 - 9$$ Simplify: $$2 - 9 = -7$$ 4. **Write the full simplified fraction:** $$\frac{16 + 9x}{-7}$$ 5. **Optional: Express with negative sign in numerator:** $$\frac{16 + 9x}{-7} = -\frac{16 + 9x}{7}$$ **Final answer:** $$-\frac{16 + 9x}{7}$$