The problem in the image is:

$1 \cdot (-2)^3 \cdot (-2)^4$

Let's solve it step by step:

Step 1: Simplify each term

1. $(-2)^3 = -8$ because: $(-2) \cdot (-2) \cdot (-2) = -8$
2. $(-2)^4 = 16$ because: $(-2) \cdot (-2) \cdot (-2) \cdot (-2) = 16$

Step 2: Combine using multiplication

Now multiply all terms together: $1 \cdot (-8) \cdot 16 = -128$

Final Answer:

$\boxed{-128}$

Would you like a detailed breakdown or have any related questions?

Related Questions:

1. What happens if you multiply more powers of $(-2)$?
2. How do negative exponents affect the result of such problems?
3. What is the general rule for multiplying terms with the same base (e.g., $(-2)^3 \cdot (-2)^4$)?
4. How does the sign of a number affect the powers?
5. How do odd and even powers differ in their results for negative bases?

Tip:

When multiplying powers with the same base, you can add the exponents:
$a^m \cdot a^n = a^{m+n}$