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The expression given is \( \left( 16^{\frac{1}{4}} \right)^5 \).

### Step-by-Step Solution:

1. **Simplify the base exponent:**
   \( 16^{\frac{1}{4}} \) represents the fourth root of 16. Since \( 16 = 2^4 \), we can rewrite:
   \[
   16^{\frac{1}{4}} = (2^4)^{\frac{1}{4}} = 2
   \]

2. **Apply the outer exponent:**
   Now we raise \( 2 \) to the power of 5:
   \[
   \left( 16^{\frac{1}{4}} \right)^5 = 2^5 = 32
   \]

Thus, the expression \( \left( 16^{\frac{1}{4}} \right)^5 \) simplifies to **32**.

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### 5 Related Questions:
1. How do you simplify expressions involving fractional exponents?
2. What is the general process for simplifying radical expressions?
3. How do powers and roots relate when simplifying expressions?
4. What are the properties of exponents used in simplifying powers of radicals?
5. How would the expression change if it was \( \left( 16^{\frac{1}{2}} \right)^5 \)?

**Tip:** Always remember to simplify the radical first before applying any outer exponents for easier calculation!

Express \(\left(16^{1/4}\right)^5\) in simplest radical form.

Learn how to simplify \(\left(16^{1/4}\right)^5\) using exponent rules and radical simplification techniques. This problem demonstrates the relationship between powers and roots, making it ideal for students in grades 9-12.

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