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The problem asks for the result of the following expression:

\[
(-2)^7 \cdot \left( -\frac{1}{2} \right)^{-4} \cdot \left( 2^{-3} \right)^3
\]

Let's solve it step by step:

1. **First Term**: 
   \[
   (-2)^7 = -128
   \]
   This is because \( (-2)^7 = -2 \times -2 \times -2 \times -2 \times -2 \times -2 \times -2 = -128 \).

2. **Second Term**: 
   \[
   \left( -\frac{1}{2} \right)^{-4} = \left( -2 \right)^4 = 16
   \]
   Raising a fraction to a negative power flips the fraction and applies the exponent: \( \left( -\frac{1}{2} \right)^{-4} = (-2)^4 = 16 \).

3. **Third Term**:
   \[
   \left( 2^{-3} \right)^3 = 2^{-9}
   \]
   This is because \( \left( 2^{-3} \right)^3 = 2^{-3 \times 3} = 2^{-9} \). We leave this in exponential form for now.

Now, multiply all terms together:

\[
-128 \cdot 16 \cdot 2^{-9}
\]

First, calculate \( -128 \cdot 16 \):

\[
-128 \cdot 16 = -2048
\]

Now include \( 2^{-9} \):

\[
-2048 \cdot 2^{-9} = \frac{-2048}{2^9}
\]

Since \( 2^9 = 512 \):

\[
\frac{-2048}{512} = -4
\]

So, the result of the expression is \( \boxed{-4} \).

---

Do you want further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do negative exponents affect fractions?
2. Why does flipping the fraction work with negative exponents?
3. What happens when you multiply powers of 2 with different exponents?
4. What is the general rule for dealing with negative bases raised to odd powers?
5. How do you simplify an expression with multiple powers?

**Tip**: Always simplify powers of the same base first before multiplying the numbers.

Learn how to solve the exponential expression (-2)^7 * (-1/2)^-4 * (2^-3)^3 step by step. This problem covers exponentiation concepts, including negative exponents and multiplication of powers. Suitable for high school students (Grades 9-12).

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