Let's break down the expression step by step.

You provided the expression:

\[
\frac{w^2}{w^{2-4}} - \frac{1}{w-2}
\]

### Step 1: Simplify the first term
The first term is:

\[
\frac{w^2}{w^{2-4}} = \frac{w^2}{w^{-2}} = w^{2 - (-2)} = w^{2+2} = w^4
\]

So, the expression now becomes:

\[
w^4 - \frac{1}{w-2}
\]

### Step 2: Final expression
This simplifies the expression to:

\[
w^4 - \frac{1}{w-2}
\]

### Final Answer:
\[
w^4 - \frac{1}{w-2}
\]

Would you like further clarification or have any questions?

### 5 Related Questions:
1. How do you handle exponents with negative values?
2. What is the general rule for simplifying expressions with exponents?
3. How can this expression be solved for specific values of \( w \)?
4. How does one simplify complex rational expressions?
5. What happens when \( w = 2 \) in the final expression?

### Tip:
When simplifying expressions with exponents, always remember that dividing terms with the same base involves subtracting their exponents.

This guide provides a detailed solution to the problem of simplifying the expression w^2/(w^(2-4)) - 1/(w-2). The solution explains key algebraic concepts such as exponentiation and rational expressions, making it ideal for students in Grades 9-10.

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