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The simplified expression is:

\[
\frac{x^6 y^2 z^4}{225}
\]

Would you like further details or have any questions about this solution?

Here are 5 related questions for practice:
1. How would the expression change if the power on \( y \) inside the parentheses was different?
2. Can you simplify \( \left( \frac{a^2 b}{c^3} \times \frac{d^{-1} c^2}{b^2} \right)^3 \)?
3. What happens if the exponent outside the parentheses is negative instead of positive?
4. How do you handle simplifying an expression with multiple variables raised to negative exponents?
5. How does the constant factor affect the simplification process when raised to a power?

**Tip**: When simplifying expressions with multiple variables and exponents, always deal with each term separately before combining like terms.

Simplify \left(\frac{y^2}{5z}\right)\left(\frac{x^3 y^{-1}}{3z^{-3}}\right)^2

Learn how to simplify the expression \left(\frac{y^2}{5z}\right)\left(\frac{x^3 y^{-1}}{3z^{-3}}\right)^2. This algebraic problem involves the use of exponent rules, multiplication of fractions, and simplification techniques. Suitable for high school students (Grades 9-12).

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