The expression shown is $4^{-3/2}$.

We can simplify this step by step:

1. First, recognize that a negative exponent indicates the reciprocal, so: $4^{-3/2} = \frac{1}{4^{3/2}}$

2. Now, express $4^{3/2}$ as a power: $4^{3/2} = (4^{1/2})^3 = ( \sqrt{4})^3$

3. Since $\sqrt{4} = 2$, we have: $4^{3/2} = 2^3 = 8$

4. Therefore: $4^{-3/2} = \frac{1}{8}$

So, the answer is $\frac{1}{8}$.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand on this concept:

1. How do you simplify other negative fractional exponents like $9^{-1/2}$?
2. What are the general rules for working with fractional exponents?
3. How does $4^{3/2}$ differ from $4^{2/3}$, and how do you compute both?
4. How can negative exponents be applied in solving real-world problems?
5. What is the relationship between exponents and roots?

Tip: When simplifying fractional exponents, always try to break them into a root and a power for easier calculation.