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To express \( 64x^9 \) as the cube of a monomial, we need to rewrite it in the form \( (a x^b)^3 \), where \( a \) and \( b \) are constants.

### Step-by-Step Solution:

1. Recognize that \( 64 \) is a perfect cube:  
   \[
   64 = 4^3
   \]
   
2. For the variable part, \( x^9 \), we can express the exponent 9 as 3 times another number:  
   \[
   x^9 = (x^3)^3
   \]

3. Now, combining these two, we can write the entire expression as:  
   \[
   64x^9 = (4x^3)^3
   \]

Thus, the expression \( 64x^9 \) can be written as the cube of the monomial \( (4x^3)^3 \).

Would you like more details or clarification on this? 

Here are some related questions to explore:
1. How do you find cube roots of larger numbers?
2. What is a monomial, and how does it differ from a polynomial?
3. How would you cube a binomial instead of a monomial?
4. Can you explain why \( 64 = 4^3 \)?
5. How does the exponent rule \( (x^m)^n = x^{m \cdot n} \) work in other examples?

**Tip:** When factoring an expression, it's helpful to look for perfect powers (like perfect squares or cubes) to simplify expressions.

Write the expression as the cube of a monomial: 64x^9

Learn how to express 64x^9 as the cube of a monomial. This problem demonstrates key algebraic concepts like exponents, cube roots, and rewriting expressions in a simplified form. Suitable for students in Grades 8-10.

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