To simplify the expression \(\left(\frac{2a^3}{3y^3}\right) \times \left(\frac{6y^3}{16x^2}\right)\), follow these steps:

1. **Multiply the numerators:**
   \[
   2a^3 \times 6y^3 = 12a^3y^3
   \]

2. **Multiply the denominators:**
   \[
   3y^3 \times 16x^2 = 48y^3x^2
   \]

3. **Combine the fractions:**
   \[
   \frac{12a^3y^3}{48y^3x^2}
   \]

4. **Simplify the fraction:**
   - First, cancel out the \(y^3\) from both the numerator and the denominator:
     \[
     \frac{12a^3\cancel{y^3}}{48\cancel{y^3}x^2} = \frac{12a^3}{48x^2}
     \]
   - Next, simplify the numerical coefficient \(\frac{12}{48}\):
     \[
     \frac{12}{48} = \frac{1}{4}
     \]
   - Therefore, the simplified expression is:
     \[
     \frac{a^3}{4x^2}
     \]

So, the simplified expression is \(\boxed{\frac{a^3}{4x^2}}\).

Would you like more details on any step, or do you have further questions?

Here are some related questions you might find helpful:
1. How do you simplify a fraction involving variables?
2. What are the rules for canceling terms in a fraction?
3. How do you multiply fractions with variables?
4. How can you factor common terms in algebraic expressions?
5. What are some tips for simplifying complex algebraic fractions?

**Tip:** Always look for common factors in the numerator and denominator to simplify fractions more easily.

Learn how to simplify the algebraic expression (2a³/3y³)*(6y³/16x²) with a detailed step-by-step breakdown. This solution covers key concepts in algebra, including multiplication of fractions and simplification of rational expressions. Suitable for students in Grades 8-10.

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