Apologies for the confusion. Let's clarify that step in the solution.

### Explanation for Step 2:

After multiplying both sides of the original equation by 8, we obtained:

\[
\sqrt[3]{4^{5-x}} = \frac{8}{2^{2x+1}}.
\]

Here, \(8\) can be rewritten as \(2^3\), so:

\[
\frac{8}{2^{2x+1}} = \frac{2^3}{2^{2x+1}}.
\]

Using the properties of exponents, specifically \(\frac{a^m}{a^n} = a^{m-n}\), we subtract the exponents:

\[
\frac{2^3}{2^{2x+1}} = 2^{3 - (2x + 1)}.
\]

Simplifying the exponent:

\[
3 - (2x + 1) = 3 - 2x - 1 = 2 - 2x.
\]

Thus, we have:

\[
\sqrt[3]{4^{5-x}} = 2^{2 - 2x}.
\]

This expression, \(2 - 2x\), comes directly from simplifying the exponent in the step where we combined the powers of 2.

Would you like any more details or have further questions?

### Related Questions
1. What are the rules of exponent subtraction in similar cases?
2. How does the expression \(2 - 2x\) impact the final solution for \(x\)?
3. Can you explain other properties of exponents used in solving such equations?
4. What if the original equation had a different base instead of 4?
5. How would the process differ if the equation had been set equal to \(3^{2x+1}\) instead?
6. Could there be another approach to simplifying the right-hand side of the equation?
7. What is the significance of isolating the exponential term in equations?
8. How would the problem change if the cube root were a fourth root instead?

### Tip
Always ensure to correctly apply and simplify the exponent rules when dealing with fractional exponents and expressions, as small mistakes can lead to incorrect results.

Explore the solution process for the equation involving exponents: 4^(5-x) = 8 / 2^(2x+1). Learn step-by-step how to simplify and solve such equations, focusing on exponent properties and algebraic manipulations. Suitable for high school students and anyone interested in mastering exponent rules in equations.

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