The expression in the image is:

$\left( (-16)^2 \right)^{-\frac{1}{8}}$

Let's solve it step by step.

Step 1: Simplify the inside of the parentheses

We first calculate $(-16)^2$. Squaring $-16$ gives:

$(-16)^2 = 256$

Step 2: Apply the outer exponent

Now we have:

$256^{-\frac{1}{8}}$

This expression is the 8th root of 256, raised to the power of $-1$. The 8th root of 256 is 2, because:

$2^8 = 256$

So,

$256^{\frac{1}{8}} = 2$

Step 3: Apply the negative exponent

The negative exponent $-1$ means taking the reciprocal:

$256^{-\frac{1}{8}} = \frac{1}{2}$

Final Answer:

The result of the given expression is:

$\frac{1}{2}$

Would you like further details on any part of the solution, or have any other questions?

Here are 5 related questions you can explore:

1. What happens when we apply a negative exponent to any number?
2. How can we calculate the nth root of a number efficiently?
3. How does changing the exponent affect the outcome of the equation?
4. What is the general rule for powers of negative numbers?
5. How do fractional exponents relate to roots?

Tip: Always check for negative exponents, as they indicate a reciprocal of the base raised to the positive exponent.