https://file.aiquickdraw.com/mathbot/file/1726135125705aw4xx2rx.jpg

Let's simplify the given expression step by step:

The expression is:

\[
\frac{w^3z}{(wz)^2z^3}
\]

### Step 1: Expand the denominator
The term \((wz)^2\) means that both \(w\) and \(z\) are squared. So,

\[
(wz)^2 = w^2z^2
\]

Thus, the denominator becomes:

\[
w^2z^2z^3
\]

Now simplify the \(z\) terms in the denominator:

\[
z^2z^3 = z^{5}
\]

So the full expression becomes:

\[
\frac{w^3z}{w^2z^5}
\]

### Step 2: Simplify the expression
Now, simplify the \(w\) and \(z\) terms individually:

- For \(w\), subtract the exponents: \(w^3 / w^2 = w^{3-2} = w^1 = w\)
- For \(z\), subtract the exponents: \(z / z^5 = z^{1-5} = z^{-4}\)

So the simplified expression is:

\[
\frac{w}{z^4}
\]

Thus, the correct simplified form is:

\[
\boxed{\frac{w}{z^4}}
\]

Let me know if you'd like further clarification!

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Here are 5 related questions to help you explore this topic further:
1. How do you simplify expressions with negative exponents?
2. What is the rule for distributing exponents over products like \((wz)^2\)?
3. How do you handle division with variables raised to powers?
4. Can you explain the laws of exponents in more detail?
5. How do you approach simplifying more complex algebraic fractions?

**Tip:** When simplifying expressions with multiple variables, always deal with one variable at a time and apply exponent rules carefully.

Simplify the expression \( \frac{w^3z}{(wz)^2z^3} \) to its simplest form.

Learn how to simplify the algebraic expression \( \frac{w^3z}{(wz)^2z^3} \) step-by-step, applying exponent rules and simplifying powers of variables. This problem explores key concepts in exponents and algebra, suitable for students in Grades 9-11.

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