Simplify:
left parenthesis, 2, r, cubed, right parenthesis, cubed
(2r 
3
 ) 
3
 

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

1. Apply the power of a power rule, which states \((a^m)^n = a^{m \cdot n}\).
   
   So, we can rewrite this as:
   \[
   2^3 \cdot (r^3)^3
   \]

2. Simplify each part:
   - \(2^3 = 8\)
   - \((r^3)^3 = r^{3 \cdot 3} = r^9\)

3. Combine the results:
   \[
   8r^9
   \]

### Final Answer:
\[
(2r^3)^3 = 8r^9
\]

Would you like more details or have any questions? 

Here are some related questions to explore this concept further:
1. How do you simplify \((3x^4)^2\)?
2. What is the result of \((5y^2)^4\)?
3. Can you simplify \((3a^3b)^2\)?
4. How does the power of a power rule work with fractional exponents?
5. What is the general formula for \((k \cdot x^m)^n\)?

**Tip:** When raising a product to a power, raise each term within the parentheses to that power separately.

Learn how to simplify the exponential expression (2r^3)^3 with a detailed solution. This problem explores the power of a power rule in exponents, breaking down each step to show how to arrive at the final answer, 8r^9. Suitable for students in Grades 8-10.

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