1. **State the problem:** Solve the equation $$2^{x+4} = 2^{(x+5)3}$$ for $x$. 2. **Recall the property of exponents:** If $$a^m = a^n$$ and $$a > 0, a \neq 1$$, then $$m = n$$. 3. **Apply the property:** Since the bases are the same (2), set the exponents equal: $$x + 4 = (x + 5)3$$ 4. **Expand the right side:** $$x + 4 = 3x + 15$$ 5. **Rearrange to isolate $x$:** $$x + 4 - 3x = 15$$ $$\cancel{x} + 4 - 3\cancel{x} = 15$$ $$-2x + 4 = 15$$ 6. **Subtract 4 from both sides:** $$-2x + 4 - 4 = 15 - 4$$ $$-2x = 11$$ 7. **Divide both sides by -2:** $$\frac{-2x}{\cancel{-2}} = \frac{11}{\cancel{-2}}$$ $$x = -\frac{11}{2}$$ **Final answer:** $$x = -\frac{11}{2}$$