1. **State the problem:** Simplify the expression $$-( -3 - 2) + 4(-2) + \frac{1}{-2^{-3}} - (-2)^{-3}$$. 2. **Recall important rules:** - Negative signs distribute over parentheses: $$-(a - b) = -a + b$$. - Powers with negative exponents: $$a^{-n} = \frac{1}{a^n}$$. - Multiplying and dividing powers: simplify carefully. 3. **Simplify inside the parentheses:** $$-( -3 - 2) = -( -5) = 5$$ 4. **Calculate the next term:** $$4(-2) = -8$$ 5. **Simplify the fraction:** $$\frac{1}{-2^{-3}} = \frac{1}{\frac{1}{-2^3}} = \frac{1}{\frac{1}{-8}} = -8$$ 6. **Simplify the last term:** $$(-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8}$$ 7. **Put all parts together:** $$5 + (-8) + (-8) - \left(-\frac{1}{8}\right) = 5 - 8 - 8 + \frac{1}{8}$$ 8. **Combine like terms:** $$5 - 8 - 8 = -11$$ 9. **Add the fraction:** $$-11 + \frac{1}{8} = -\frac{88}{8} + \frac{1}{8} = -\frac{87}{8}$$ **Final answer:** $$-\frac{87}{8}$$