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The problem asks to simplify the following expression:

\[
\left( \frac{x^3 y^6}{x^5 y^{-2}} \right)^4
\]

Let's simplify this step by step.

### Step 1: Simplify inside the parentheses

We have:

\[
\frac{x^3 y^6}{x^5 y^{-2}}
\]

Using the properties of exponents, subtract the exponents for both \(x\) and \(y\):

- For \(x\), we subtract the exponents: \(3 - 5 = -2\)
- For \(y\), we subtract the exponents: \(6 - (-2) = 6 + 2 = 8\)

Thus, we now have:

\[
x^{-2} y^8
\]

### Step 2: Apply the power of 4

Now, apply the exponent of 4 to the simplified expression:

\[
\left( x^{-2} y^8 \right)^4
\]

This results in multiplying each exponent by 4:

- \(x^{-2} \to x^{-8}\)
- \(y^8 \to y^{32}\)

Thus, the expression becomes:

\[
x^{-8} y^{32}
\]

### Final Answer:

\[
\boxed{x^{-8} y^{32}}
\]

This is the simplified form of the given expression.

Do you have any questions or need further details?

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Here are some related questions for deeper understanding:
1. How do you apply the laws of exponents when dividing powers with the same base?
2. What happens when you raise a power to another power?
3. How would the answer change if the base was negative?
4. Can you express \(x^{-8}\) without using negative exponents?
5. How would you simplify a similar expression involving cube roots instead of powers?

**Tip:** Always simplify inside parentheses first before applying any outside exponents or other operations.

Sederhanakan bentuk pangkat berikut: (x^3 * y^6) / (x^5 * y^-2))^4

Learn how to simplify the exponent expression (x^3 * y^6) / (x^5 * y^-2))^4 with step-by-step solutions. This problem covers key algebraic concepts such as exponent rules and division of powers, suitable for students in Grades 9-11.

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