To multiply the expressions \( (2x^3) \) and \( (5x^6) \), we use the rules of multiplication for constants and powers of the same base.

1. **Multiply the coefficients (constants):**
   - The coefficients are 2 and 5. So, \( 2 \times 5 = 10 \).

2. **Multiply the variables with the same base (x):**
   - When multiplying variables with the same base, you add the exponents. So, for \( x^3 \) and \( x^6 \), you add the exponents: \( 3 + 6 = 9 \).

Putting it all together:

\[
(2x^3)(5x^6) = 10x^{3+6} = 10x^9
\]

So, the product is \( \boldsymbol{10x^9} \).

Would you like further clarification, or do you have any other questions on this topic?

Here are some related questions you might find helpful:
1. How do you multiply monomials with different bases?
2. What is the power of a product rule in exponents?
3. How do you simplify the product of two binomials?
4. How do you handle multiplication of polynomials with negative exponents?
5. What is the distributive property and how is it applied in polynomial multiplication?
6. How do you divide monomials?
7. What are like terms, and why is it important to combine them?
8. How can you use the FOIL method to multiply binomials?

**Tip:** Always keep track of the signs and exponents when multiplying polynomials, as mistakes in these areas are common.

Learn how to multiply the expressions (2x^3)(5x^6) with a detailed step-by-step solution. This problem covers key algebraic concepts such as multiplication of monomials and exponents. Suitable for students in Grades 7-9.

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