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The given mathematical expression simplifies to:

\[
\frac{0.2887}{m^9 y^{16} X^{1.5} \sqrt{m^2}}
\]

This is a simplified version of the original expression where numerical constants and exponents have been reduced.

Would you like further clarification or details on any step? Here are five related questions that might expand your understanding:

1. How are fractional exponents handled when simplifying powers of variables?
2. What are the steps to simplify expressions involving multiple powers and products?
3. How can we interpret constants like 0.2887 in terms of their roots?
4. How does dividing by a negative exponent affect the overall expression?
5. What techniques are useful for simplifying complex algebraic fractions?



Simplify the given algebraic expression involving exponents, variables, and constants: ( (3^(-1/6) * X^(-1/3)) / (y^6 * m^(3)) )^3 * ((X^(-1) * m^(-2))^(-1/2)) / (2 * y^(-2)).

This example demonstrates how to simplify a complex algebraic expression involving variables X, y, and m, with fractional and negative exponents. Using the laws of exponents, we break down each term step by step, ultimately simplifying the expression to a more manageable form.

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