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To simplify \((2x^3y^2)^3\), follow these steps:

1. Apply the power rule \((a^m)^n = a^{m \cdot n}\):
   \[
   (2x^3y^2)^3 = 2^3 \cdot (x^3)^3 \cdot (y^2)^3
   \]

2. Simplify each component:
   \[
   2^3 = 8, \quad (x^3)^3 = x^{3 \cdot 3} = x^9, \quad (y^2)^3 = y^{2 \cdot 3} = y^6
   \]

3. Combine the results:
   \[
   8x^9y^6
   \]

The correct answer is **(c) \(8x^9y^6\)**.

Would you like to delve deeper into any step? Here are five related questions:

1. How do exponent rules apply to bases with coefficients like \(2\)?
2. What happens if one of the exponents was negative in the original problem?
3. How would this change if the base contained a division instead of multiplication?
4. Can you apply the same steps if \(y\) had fractional exponents?
5. Why is it important to multiply powers rather than add them here?

**Tip:** Always handle coefficients separately from variables when simplifying expressions with exponents!

Simplify (2x^3y^2)^3 and choose the correct answer.

Discover how to simplify the expression (2x^3y^2)^3 using the power rule of exponents. A detailed step-by-step guide explains how to handle coefficients and variables. Perfect for Grades 9-10 students.

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