https://file.aiquickdraw.com/mathbot/file/1726795558106udhe7v2p.jpg

The question in the image asks to:

1. **Write** \((4n^4)^2\) **without exponents**.
2. **Fill in the blanks** for the expression \((4n^4)^2 = 16n^{\_}\).

### Let's break it down:

1. **Without Exponents:**
   \[
   (4n^4)^2 = 4^2 \cdot (n^4)^2
   \]
   - \(4^2 = 16\)
   - \((n^4)^2 = n^{4 \cdot 2} = n^8\)
   
   So, the expression without exponents would be:
   \[
   16n^8
   \]

2. **Fill in the blanks:**
   The result is:
   \[
   (4n^4)^2 = 16n^8
   \]

The missing exponent in the blank is **8**.

Would you like more detailed steps or have any other questions?

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Here are 5 related questions to explore:
1. How would you expand \((3n^5)^3\)?
2. What is the result of \((2a^3b^2)^4\)?
3. How do you simplify \((x^7)^3\)?
4. Can you rewrite \((5m^2n^3)^2\) without using exponents?
5. What is the exponent rule for raising a power to another power?

**Tip:** Remember, when raising a power to a power, multiply the exponents!

Write (4n^4)^2 without exponents and fill in the blanks for (4n^4)^2 = 16n^_ .

Learn how to apply the power of a power rule in exponents by expanding (4n^4)^2. This problem demonstrates how to write exponents without powers and simplify algebraic expressions using exponent rules. Suitable for students in Grades 8-10.

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