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The given operation simplifies to:

\[
\sqrt[6]{(12^{15})(12)(12^8)(x^{12})} = 20736 \cdot x^2
\]

Thus, the final result of the operation is:

\[
20736 \cdot x^2
\]

The correct answer depends on the value assigned to \( x \), but based on the structure of the provided options, the closest matching form would be the one including \( 144 \), since \( 144 \times x^2 \) could represent a specific numerical substitution for \( x \).

Would you like to ask anything about this solution or further details? Here are 5 related questions for you to explore:

1. How do we simplify powers when multiplying terms with the same base?
2. What happens when we take the 6th root of an expression like \( x^{12} \)?
3. Can we further simplify \( 20736 \cdot x^2 \) in terms of specific values for \( x \)?
4. How do we approach finding roots of large powers and products like this?
5. What is the significance of the \( x^2 \) term in this context?

**Tip:** Always check if you can simplify the powers and roots before evaluating the entire expression!

Calcule el resultado de la siguiente operación: \sqrt[6]{(12^{15})(12)(12^8)(x^{12})}

Learn how to calculate the 6th root of a product involving exponents: \sqrt[6]{(12^{15})(12)(12^8)(x^{12})}. This problem explores key exponent laws and simplification techniques, suitable for high school students in Grades 10-12.

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