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The expression you've provided is \(\left( \sqrt{y} \right)^{4y}\). Let's break it down and express it using exponents and fractions.

1. \(\sqrt{y}\) can be written as \(y^{1/2}\) (since the square root is the same as raising to the power of \(1/2\)).
2. Therefore, the entire expression becomes:
   \[
   \left( y^{1/2} \right)^{4y}
   \]
3. To simplify this, use the rule \((a^m)^n = a^{m \cdot n}\), which allows us to multiply the exponents:
   \[
   y^{\left( \frac{1}{2} \cdot 4y \right)} = y^{2y}
   \]

Thus, the simplified expression is \(y^{2y}\).

Would you like a further explanation of any of these steps?

Here are 5 related questions you could explore:
1. How do you simplify expressions involving fractional exponents?
2. What are the general rules for working with exponents?
3. How do you solve equations that contain exponents and roots?
4. What is the difference between rational and irrational exponents?
5. How do you solve logarithmic equations derived from exponential expressions?

**Tip:** When simplifying exponents, always look for rules that allow you to combine or manipulate powers efficiently, like \((a^m)^n = a^{m \cdot n}\).

Learn how to simplify the expression (√y)^(4y) using exponents and radicals. This problem involves understanding the conversion of square roots into fractional exponents and applying the power of a power rule. Suitable for students in Grades 9-10.

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