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To solve \( \left(4y^4\right)^2 \) without using exponents, we can apply the power rule for exponents, which states that \( (a^m)^n = a^{m \cdot n} \).

1. Expand the expression using the rule:
   \[
   \left(4y^4\right)^2 = 4^2 \cdot (y^4)^2
   \]

2. Calculate \( 4^2 \):
   \[
   4^2 = 16
   \]

3. Apply the power rule to \( (y^4)^2 \):
   \[
   (y^4)^2 = y^{4 \cdot 2} = y^8
   \]

4. Combine the results:
   \[
   \left(4y^4\right)^2 = 16y^8
   \]

**Answer:** The expression without exponents is \( 16y^8 \).

Would you like further details, or do you have additional questions?

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Here are some related questions to expand on the topic:

1. How does the power rule for exponents work with negative exponents?
2. What is the general form of the power rule when there are multiple variables?
3. How would you simplify \( \left(3x^2y^3\right)^4 \)?
4. Can the power rule be applied to fractional exponents?
5. What happens when the exponent is zero in expressions like \( (a^m)^0 \)?

**Tip:** When applying the power rule, remember to multiply the exponents to keep the expression simplified.

Learn how to simplify the expression (4y^4)^2 without using exponents by applying the power rule. This solution breaks down each step, including expanding terms and combining powers. Ideal for students in Grades 8-10 exploring exponents and power rules in algebra.

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