The expression in the image you uploaded is:

$\left( \frac{2m^2n^{-1}}{n^2} \right)^3$

Let's simplify this step by step.

Step 1: Simplify the expression inside the parentheses.

The expression inside the parentheses is:

$\frac{2m^2n^{-1}}{n^2}$

Since $n^{-1}$ means $\frac{1}{n}$, we can rewrite this as:

$\frac{2m^2}{n \cdot n^2} = \frac{2m^2}{n^3}$

Step 2: Apply the exponent of 3.

Now, we raise the entire fraction to the power of 3:

$\left( \frac{2m^2}{n^3} \right)^3 = \frac{(2m^2)^3}{(n^3)^3}$

Step 3: Simplify the powers.

$(2m^2)^3 = 2^3 \cdot (m^2)^3 = 8m^6$

$(n^3)^3 = n^{3 \times 3} = n^9$

Final simplified expression:

$\frac{8m^6}{n^9}$

Would you like further explanation on any of the steps or have any questions about this process? Here are 5 related questions to deepen your understanding:

1. How do you simplify expressions with negative exponents like $n^{-1}$?
2. What is the rule for simplifying powers of a product, like $(ab)^n$?
3. How do you handle the exponentiation of a fraction in general?
4. What would happen if the original expression had a different power, say 2 instead of 3?
5. How can this type of expression be applied in real-world scenarios, such as physics or engineering?

Tip: When dealing with negative exponents, it's always useful to rewrite them as fractions to make simplification easier.