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We are tasked with solving the equation:

\[
2^{3x - 4} = \frac{1}{128^{4 - x}}
\]

### Step 1: Simplify the right-hand side

We know that \( 128 = 2^7 \), so:

\[
128^{4 - x} = (2^7)^{4 - x} = 2^{7(4 - x)} = 2^{28 - 7x}
\]

Thus, the equation becomes:

\[
2^{3x - 4} = \frac{1}{2^{28 - 7x}} = 2^{-(28 - 7x)}
\]

### Step 2: Set the exponents equal

Since both sides are powers of 2, we can equate the exponents:

\[
3x - 4 = -(28 - 7x)
\]

### Step 3: Solve for \( x \)

First, distribute the negative sign on the right-hand side:

\[
3x - 4 = -28 + 7x
\]

Now, bring all terms involving \( x \) to one side:

\[
3x - 7x = -28 + 4
\]

\[
-4x = -24
\]

Solve for \( x \):

\[
x = \frac{-24}{-4} = 6
\]

Thus, the solution is \( x = 6 \).

### Final Answer:
The correct option is:
\[
\boxed{c. \ 6}
\]

---

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Solve \( 3^{x+2} = 27^{x-1} \).
2. Simplify and solve \( 5^{2x} = 25^{x+1} \).
3. Solve \( 4^{x-3} = 64^{x-4} \).
4. Find the solution to \( 2^{x+1} = 8^{2x-3} \).
5. Solve for \( x \) in \( 9^{x-2} = 81^{3x-5} \).

**Tip:** When dealing with equations involving exponents, it's often helpful to express all terms with the same base for easier manipulation.

Solve the equation 2^(3x - 4) = 1 / 128^(4 - x).

Learn how to solve the exponential equation 2^(3x - 4) = 1 / 128^(4 - x) with a detailed step-by-step solution. This problem demonstrates exponent rules and algebraic manipulation, suitable for Grades 10-12 students.

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