## Simplifying the Expression (m^3n^2/2m)^4^3

This problem involves simplifying an expression with exponents and fractions. Let's break it down step-by-step:

### 1. Simplifying the Inner Expression

First, we'll simplify the expression inside the parentheses:

**m^3 / m = m^(3-1) = m^2**

Now the expression becomes:

**(m^2n^2 / 2)^4^3**

### 2. Simplifying the Exponents

We need to deal with the exponents, starting from the innermost:

**4^3 = 4 * 4 * 4 = 64**

The expression now looks like:

**(m^2n^2 / 2)^64**

### 3. Applying the Power of a Quotient Rule

The power of a quotient rule states that **(a/b)^n = a^n / b^n**. Applying this rule, we get:

**(m^2n^2)^64 / 2^64**

### 4. Applying the Power of a Product Rule

The power of a product rule states that **(ab)^n = a^n * b^n**. Applying this rule, we get:

**(m^2)^64 * (n^2)^64 / 2^64**

### 5. Simplifying Further

Finally, we simplify by multiplying the exponents:

**m^(2 64) * n^(264) / 2^64**

**m^128 * n^128 / 2^64**

### Conclusion

Therefore, the simplified form of the expression (m^3n^2/2m)^4^3 is **m^128 * n^128 / 2^64**.