Choose the correct simplification of (3xy6)2(y3)3.

To simplify the expression \((3xy^6)^2(y^3)^3\), we can follow these steps:

1. **Apply the power rule:** 
   The power rule states that \((a^m)^n = a^{m \cdot n}\). We apply this rule to each part of the expression.

2. **Simplify \((3xy^6)^2\):**
   - The coefficient \(3\) raised to the power of 2 is \(3^2 = 9\).
   - The variable \(x\) raised to the power of 2 is \(x^2\).
   - The variable \(y^6\) raised to the power of 2 is \(y^{6 \cdot 2} = y^{12}\).

   So, \((3xy^6)^2 = 9x^2y^{12}\).

3. **Simplify \((y^3)^3\):**
   - Using the power rule, \(y^3\) raised to the power of 3 is \(y^{3 \cdot 3} = y^9\).

4. **Combine the simplified parts:**
   - We now combine \(9x^2y^{12}\) and \(y^9\).

5. **Combine like terms:**
   - The coefficient remains \(9\).
   - The variable \(x\) remains \(x^2\).
   - The variable \(y\) is combined as \(y^{12} \cdot y^9 = y^{12+9} = y^{21}\).

Therefore, the simplified form of the expression is:

\[
9x^2y^{21}
\]

So, the correct simplification of \((3xy^6)^2(y^3)^3\) is \(9x^2y^{21}\).

If you have any questions or need further clarification, feel free to ask!

Here are 8 related questions you might be interested in:

1. How do you apply the power rule in other contexts?
2. What are some examples of simplifying expressions with multiple variables?
3. How do you simplify expressions involving negative exponents?
4. What is the difference between combining like terms and applying the power rule?
5. How do you simplify expressions with fractional exponents?
6. What are common mistakes when simplifying algebraic expressions?
7. How do you handle simplification of polynomials?
8. What is the role of the distributive property in simplification?

**Tip:** Always remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions. This will help ensure accuracy in your calculations.

Learn how to simplify the expression (3xy^6)^2(y^3)^3 step-by-step with detailed explanations. This problem involves exponentiation and variables, suitable for students in Grades 7-9.

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