To simplify the expression \((16x^4y^5)^{\frac{1}{4}}\), follow these steps:

### Step 1: Apply the exponent to each factor inside the parentheses.

The expression is \((16x^4y^5)^{\frac{1}{4}}\). The exponent \(\frac{1}{4}\) applies to each component:

\[
(16)^{\frac{1}{4}} \cdot (x^4)^{\frac{1}{4}} \cdot (y^5)^{\frac{1}{4}}
\]

### Step 2: Simplify each term separately.
- \( (16)^{\frac{1}{4}} = \sqrt[4]{16} = 2 \) since \(2^4 = 16\).
- \( (x^4)^{\frac{1}{4}} = x^{\frac{4}{4}} = x^1 = x \).
- \( (y^5)^{\frac{1}{4}} = y^{\frac{5}{4}} \).

### Final Expression:
\[
2x y^{\frac{5}{4}}
\]

So, \((16x^4y^5)^{\frac{1}{4}} = 2x y^{\frac{5}{4}}\).

Would you like more details on the simplification process or have any questions?

### Related Questions:
1. How do you simplify expressions with different exponents?
2. What is the process for simplifying \((9a^2b^8)^{\frac{1}{2}}\)?
3. How do you find the fourth root of a number?
4. How do you handle fractional exponents in algebraic expressions?
5. What are the rules for multiplying and dividing exponents?

### Tip:
When simplifying expressions with exponents, always break down the expression and apply the exponent rules step by step to each part.

Learn how to simplify the expression (16x^4y^5)^(1/4) step-by-step. This problem involves applying exponentiation and radical simplification rules to simplify complex expressions. Suitable for students in Grades 7-9 studying exponents and radicals.

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