Question: Use the order of operations to find the value of the following ex
[ -4^2 + (3 - 5)^3 - (-5) ] - [ |-3|^2 + 2 - 2^3 ]
1. **State the problem:**
Find the value of the expression $$[ -4^2 + (3 - 5)^3 - (-5) ] - [ |-3|^2 + 2 - 2^3 ]$$ using the order of operations.
2. **Recall the order of operations:**
- Parentheses and absolute values first
- Exponents next
- Multiplication and division from left to right
- Addition and subtraction from left to right
3. **Evaluate inside the first bracket:**
- Calculate $$-4^2$$: Note that exponentiation comes before the negative sign, so $$-4^2 = -(4^2) = -16$$.
- Calculate $$(3 - 5)^3$$:
$$3 - 5 = -2$$
$$(-2)^3 = -8$$
- Calculate $$-(-5) = +5$$
So the first bracket becomes:
$$-16 + (-8) + 5$$
4. **Simplify the first bracket:**
$$-16 - 8 + 5 = (-16 - 8) + 5 = -24 + 5 = -19$$
5. **Evaluate inside the second bracket:**
- Calculate $$|-3|^2$$:
$$|-3| = 3$$
$$3^2 = 9$$
- Calculate $$2^3 = 8$$
So the second bracket becomes:
$$9 + 2 - 8$$
6. **Simplify the second bracket:**
$$9 + 2 - 8 = 11 - 8 = 3$$
7. **Combine both brackets:**
$$(-19) - (3) = -19 - 3 = -22$$
**Final answer:** $$\boxed{-22}$$