Let's evaluate each expression:

1. Evaluating $- (4)^3$:

   • First, we calculate $(4)^3$.
   • $4^3 = 4 \times 4 \times 4 = 64$.
   • Then, apply the negative sign: $- (4)^3 = -64$.

   So, $- (4)^3 = -64$.

2. Evaluating $(-3)^3$:

   • Here, we calculate $(-3)^3$.
   • $(-3)^3 = (-3) \times (-3) \times (-3) = -27$ (since an odd number of negatives results in a negative).

   So, $(-3)^3 = -27$.

Final Answers

• $- (4)^3 = -64$
• $(-3)^3 = -27$

Would you like any further details on this?

Here are some related questions for further exploration:

1. What is the difference between $-4^3$ and $(-4)^3$?
2. How does the sign of the base affect the result of an exponent?
3. What happens if the exponent is even instead of odd for a negative base?
4. How can exponents be applied in practical applications like area or volume?
5. Why does an odd exponent on a negative number result in a negative outcome?

Tip: When evaluating expressions with exponents, be mindful of parentheses—they change how signs are applied in calculations.