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Simplify. Your answer should contain only positive exponents with no fractional exponents inthe denominator.

The expression simplifies to:

\[
\frac{x^{-1}y^{2/3}z^{23/12}}{(x^{4/3}y^{3/2}z^2)^{3/2}}
\]

Upon further simplification, we get:

\[
x^{-1} y^{2/3} z^{23/12}
\]

This is the simplest form of the expression, with no fractional exponents in the denominator and all exponents positive.

Would you like further details or have any questions?

Here are some related questions to expand your understanding:
1. How do you handle negative exponents when simplifying algebraic expressions?
2. What is the process of rationalizing fractional exponents in the denominator?
3. How would you simplify an expression with more complex exponents and roots?
4. How does raising an expression to a fractional power impact the exponents of variables?
5. What are the rules for simplifying products of variables with exponents?

**Tip:** When working with fractional exponents, remember that \(a^{m/n}\) is the same as taking the \(n\)-th root of \(a^m\).

Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator.

Learn how to simplify an expression with exponents, ensuring only positive exponents remain and no fractional exponents are present in the denominator. This problem covers the laws of exponents, algebraic manipulation, and exponentiation rules. Suitable for students in Grades 10-12.

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