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

1. First term: $[3^2]^4 = 3^{2 \times 4} = 3^8$

2. Second term: [ [3^3] \times [3^3]^3 = 3^3 \times 3^{3 \times 3} = 3^3 \times 3^9 ] Since $3^a \times 3^b = 3^{a + b}$: $3^3 \times 3^9 = 3^{3 + 9} = 3^{12}$

3. Combine the two terms: $3^8 + 3^{12}$

This is the final expression as the sum of two powers of 3. Since they are not like terms, this expression cannot be combined into a single power.

Would you like more details on this, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How would you factor the expression $3^8 + 3^{12}$?
2. What is the difference between $(3^2)^4$ and $(3^4)^2$?
3. How would you simplify $(a^m)^n$ when $m$ and $n$ are both even?
4. How does the distributive property apply to expressions like $3^8 + 3^{12}$?
5. Can you express $(2^3)^5 + 2^{15}$ as a single power?

Tip: When multiplying powers with the same base, simply add their exponents.