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

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.

Learn how to simplify the expression [3²]⁴ + [3³]*[3³]³ step-by-step with detailed explanations and examples. This problem involves applying power rules, multiplication of powers with the same base, and addition of exponents. Suitable for students in Grades 7-9.

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