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To solve this expression, let's go through the steps to multiply and simplify:

The expression given is:
\[
\frac{6x^3}{7} \cdot \frac{4x^3}{3}
\]

### Step 1: Multiply the Numerators and Denominators
Multiply the terms in the numerator and denominator separately:
\[
\frac{6x^3 \cdot 4x^3}{7 \cdot 3} = \frac{24x^6}{21}
\]

### Step 2: Simplify the Fraction
Now, simplify \(\frac{24x^6}{21}\) by finding the greatest common divisor (GCD) of 24 and 21, which is 3:
\[
\frac{24x^6}{21} = \frac{24 \div 3 \cdot x^6}{21 \div 3} = \frac{8x^6}{7}
\]

### Final Answer
The simplified result is:
\[
\frac{8x^6}{7}
\]

Would you like a breakdown of any step or have further questions?

### Related Questions to Explore:
1. How do you multiply two fractions with variables?
2. What is the process for simplifying fractions with exponents?
3. How can we find the greatest common divisor (GCD) in fraction simplification?
4. How does the distributive property affect operations with exponents?
5. How do you handle negative exponents in similar expressions?

### Tip
When multiplying fractions, always simplify after multiplying both the numerators and denominators for a cleaner answer.

Perform the operation and simplify the answer fully: (6x^3 / 7) * (4x^3 / 3)

Simplify the algebraic expression (6x^3 / 7) * (4x^3 / 3) by performing multiplication and reducing the fraction fully. This solution covers exponent rules and fraction simplification techniques, ideal for students in Grades 7-9.

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