The simplified form of the expression from the image is:

$43046721 \cdot (a^{12} b c^3)^{\frac{8}{3}}$

Would you like more details on how this was simplified or have any other questions?

Here are 5 related questions to expand on the topic:

1. How do fractional exponents affect variables in expressions like this?
2. What are the rules for simplifying powers of powers?
3. How do you deal with negative exponents when simplifying?
4. What is the significance of using the greatest common factors in exponent rules?
5. How do you handle expressions involving multiple variables and exponents?

Tip: When simplifying exponents, always apply exponent rules in a stepwise manner to ensure accuracy.