The expression you've provided is:

$[(2^2)^3 \times 3^6] \times 5^6$

Let's break it down step by step:

1. Start with the first part: $(2^2)^3$:

   • First, calculate $2^2$, which is 4.
   • Then raise that result to the power of 3: $(2^2)^3 = 4^3 = 64$.

2. Next, multiply that by $3^6$:

   • $3^6 = 729$.

So, the expression so far is:

$64 \times 729 = 46656$

3. Now, multiply by $5^6$:
   • $5^6 = 15625$.

Finally, multiply $46656 \times 15625$:

$46656 \times 15625 = 728437500$

Final answer:

$728437500$

Would you like a more detailed explanation, or do you have any further questions about this?

Here are some related questions:

1. How would you simplify expressions with multiple exponents like this one?
2. What is the general rule for exponents when you have nested powers (like $(a^m)^n$)?
3. How can you quickly calculate powers of numbers like $3^6$ and $5^6$?
4. What would happen if the bases of the powers in the expression were negative numbers instead?
5. How do you estimate large numbers when dealing with exponents?

Tip: When dealing with exponents, remember that $(a^m)^n = a^{m \times n}$. This can save you time and help simplify the expression more quickly.