The given expression is:

\[
\frac{16x^2}{4x} \div \frac{x - 7}{4x}
\]

Let's break this down step by step:

1. **Simplify the first fraction** \(\frac{16x^2}{4x}\):
   \[
   \frac{16x^2}{4x} = 4x
   \]
   (since \(\frac{16}{4} = 4\) and \(\frac{x^2}{x} = x\)).

2. **Rewrite the division as multiplication**:
   Dividing by a fraction is equivalent to multiplying by its reciprocal. So, we rewrite the division as:
   \[
   4x \times \frac{4x}{x - 7}
   \]

3. **Multiply the numerators and the denominators**:
   \[
   4x \times \frac{4x}{x - 7} = \frac{4x \cdot 4x}{x - 7} = \frac{16x^2}{x - 7}
   \]

So, the simplified expression is:

\[
\frac{16x^2}{x - 7}
\]

Would you like more details or have any questions?

Here are some related questions you might consider:
1. How do you simplify expressions with variables in the numerator and denominator?
2. What is the process for dividing fractions?
3. How do you handle variables when multiplying fractions?
4. Can you explain why dividing by a fraction is the same as multiplying by its reciprocal?
5. What happens when there are common factors in the numerator and denominator?

**Tip:** Always simplify the expression before performing further operations like division or multiplication!

This problem demonstrates how to simplify the expression 16x^2/4x divided by (x-7)/4x using the rules of fraction division and simplification. Follow the step-by-step process for mastering algebraic fractions, appropriate for students in Grades 9-10.

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