Let's simplify the expression $[3^2]^4 + [3^3] \times [3^3]^3$ and write it as a single power of 3.

1. Simplify each part:

   • $[3^2]^4$ simplifies to $3^{2 \times 4} = 3^8$.
   • $[3^3] \times [3^3]^3$ simplifies to $3^3 \times 3^{3 \times 3} = 3^3 \times 3^9$.

2. Add the exponents of the second part:

   • $3^3 \times 3^9 = 3^{3+9} = 3^{12}$.

3. Now, combine the two terms:

   • $3^8 + 3^{12}$.

Since these are not like terms, they cannot be combined directly. However, the expression can be written as $3^8 + 3^{12}$, which is already in its simplest form.

If you were to factor this expression, you could write it as $3^8(1 + 3^4)$, but this doesn't simplify to a single power of 3 either. So, the expression $3^8 + 3^{12}$ is as simplified as it can be.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you multiply powers with the same base?
2. What is the rule for adding exponents when multiplying like bases?
3. How do you factor an expression like $3^8 + 3^{12}$?
4. How do you simplify expressions involving powers of powers?
5. Can this expression be further simplified if the bases were different?

Tip: When simplifying expressions with exponents, always apply the power rules carefully to avoid mistakes.