Let's simplify the expression:

$\frac{(2a^7)(3a^2)}{6a^3}$

Step 1: Multiply the terms in the numerator

$(2a^7)(3a^2) = 6a^{7+2} = 6a^9$

So the expression becomes: $\frac{6a^9}{6a^3}$

Step 2: Simplify the constants

The 6 in the numerator and denominator cancel out: $\frac{6a^9}{6a^3} = \frac{a^9}{a^3}$

Step 3: Apply the exponent rule for division

When dividing terms with the same base, subtract the exponents: $\frac{a^9}{a^3} = a^{9-3} = a^6$

Final Answer:

$a^6$

Would you like further details on the steps or have any questions about exponents?

Related Questions:

1. How do you simplify expressions with negative exponents?
2. What happens when you multiply or divide terms with the same base and different exponents?
3. Can you simplify expressions with fractional exponents in a similar way?
4. What is the rule for multiplying powers of the same base?
5. How do you handle powers of zero in expressions?

Tip: When dividing powers with the same base, just subtract the exponents.