The expression in the image is:

$\left(\frac{1}{4x^8}\right)^{-3}$

To simplify this expression, we can use the property of exponents that states:

$\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^{n}$

Applying this property to your expression:

$\left(\frac{1}{4x^8}\right)^{-3} = \left(\frac{4x^8}{1}\right)^{3} = (4x^8)^3$

Now, simplify further by applying the power to both the constant and the variable:

$(4x^8)^3 = 4^3 \cdot (x^8)^3 = 64 \cdot x^{24}$

So the simplified expression is:

$64x^{24}$

Would you like further details or have any questions about this solution? Here are five related questions for further exploration:

1. How do you simplify expressions with negative exponents?
2. What happens when you raise a power to another power?
3. How do you distribute an exponent over a product?
4. What is the result of simplifying $\left(\frac{1}{2x^5}\right)^{-2}$?
5. How can you rewrite $\frac{1}{x^{-2}}$ using positive exponents?

Tip: Remember that when dealing with negative exponents, inverting the base (flipping the fraction) and making the exponent positive simplifies the expression effectively.