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The expression given is:

\[
-2^{1/5} \cdot 4^{2/5}
\]

### Step 1: Simplify the powers

First, express \(4^{2/5}\) using its base:

\[
4^{2/5} = (2^2)^{2/5} = 2^{4/5}
\]

So, the expression becomes:

\[
-2^{1/5} \cdot 2^{4/5}
\]

### Step 2: Apply the exponent rules

Since the bases are the same, we can add the exponents:

\[
-2^{1/5 + 4/5} = -2^{5/5} = -2^1 = -2
\]

### Final Answer:

The expression simplifies to \(-2\).

Would you like more details or have any other questions?

### Related Questions:
1. How do you simplify expressions with fractional exponents?
2. What are the rules for multiplying exponents with the same base?
3. How would the result change if the base was negative inside the exponent?
4. Can you explain the properties of exponents further?
5. How would you solve a similar expression with different bases?

### Tip:
When working with fractional exponents, remember that they represent roots. For example, \(a^{1/n}\) is the nth root of \(a\).

Learn how to simplify the expression -2^(1/5) * 4^(2/5) step-by-step. Understand the rules of exponents and fractional exponents, and see how to apply them to simplify expressions. Suitable for high school students studying algebra and exponent rules.

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