The given expression is:

\[
16^{\frac{4}{5}} \times 8^{\frac{-2}{5}}
\]

### Step 1: Expressing the bases as powers of 2

- \( 16 = 2^4 \)
- \( 8 = 2^3 \)

Now, substitute these into the expression:

\[
(2^4)^{\frac{4}{5}} \times (2^3)^{\frac{-2}{5}}
\]

### Step 2: Simplifying the exponents

Apply the power rule \((a^m)^n = a^{m \cdot n}\):

\[
2^{4 \cdot \frac{4}{5}} \times 2^{3 \cdot \frac{-2}{5}}
\]

This simplifies to:

\[
2^{\frac{16}{5}} \times 2^{\frac{-6}{5}}
\]

### Step 3: Combining the powers of 2

Use the property \(a^m \times a^n = a^{m+n}\):

\[
2^{\frac{16}{5} + \frac{-6}{5}} = 2^{\frac{10}{5}} = 2^2
\]

### Step 4: Final result

\[
2^2 = 4
\]

Thus, the value of the expression is **4**.

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### Related Questions:
1. How do you simplify expressions with fractional exponents?
2. What is the power rule for exponents?
3. How do you combine powers with the same base?
4. Can fractional exponents be negative, and how do they behave?
5. How do you express numbers like 16 and 8 as powers of smaller numbers?

**Tip:** When dealing with fractional exponents, always try to express the base in terms of powers of smaller prime numbers, like 2 or 3, to simplify calculations.

Discover how to simplify the expression 16^(4/5) * 8^(-2/5) step by step. Learn the key exponent rules, including expressing numbers as powers of smaller numbers and simplifying fractional exponents. Suitable for high school students in Grades 9-12.

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