The image contains a mathematical expression, which I can now process. Let's break down the equation step by step:

[ \sqrt[{}]{\frac{\left(25^0\right)^3 + \frac{3}{4}}{\frac{7}{256x}}} = \sqrt[{}]{\frac{4x^2 + 256}{\sqrt[{}]{\frac{120}{5!}}^{256}}} ]

We need to solve for $x$. I'll now proceed with simplifying both sides to find the value of $x$.When simplifying both sides of the equation, assuming $x = 1$, we found:

• Left-hand side = 64
• Right-hand side = 260

Since these are not equal, it means $x \neq 1$. I will now solve the equation algebraically by adjusting for $x$ and equating both sides to find the correct value of $x$.The value of $x$ that satisfies the equation is $x = 8$.

Would you like further clarification or details on any part of the process?

Here are 5 related questions you could explore:

1. How do factorials affect complex algebraic equations?
2. What is the significance of exponents in solving radical equations?
3. How can you apply radical simplification in other math problems?
4. What steps can be used to verify if a solution is correct?
5. How do different methods of solving equations (algebraic vs. numerical) compare?

Tip: Always check for potential extraneous solutions when solving equations involving radicals.