[3²]⁴+[3³]*[3³]³ write as a single ower

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.

Explore how to simplify the expression [3²]⁴ + [3³]*[3³]³ by understanding powers of 3. This detailed explanation breaks down the terms [3²]⁴ and [3³]*[3³]³ and combines them into a single power of 3. Suitable for Grades 7-9, this math problem involves exponents and combining like terms.

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