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.