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The given expression is:

\[
N = \left( b^{-b^{b^{-b^{-b}}}} \right)^{\frac{b^b}{\sqrt[b]{\sqrt[b]{b^{-1}}}}}
\]

Let's work through the simplification step by step.

### Step 1: Simplify the inner exponent \( b^{-b^{-b^{-b}}} \)
This portion is an exponent tower, and the exponents are all negative. The negative sign will flip the fraction at each level, but we first need to deal with the exponents themselves.

### Step 2: Simplify the base expression \( b^{-b^{b^{-b^{-b}}}} \)
Since the base is raised to a negative power, it can be rewritten as a fraction:
\[
b^{-b^{b^{-b^{-b}}}} = \frac{1}{b^{b^{b^{-b^{-b}}}}}
\]

### Step 3: Simplify the outer exponent \( \frac{b^b}{\sqrt[b]{\sqrt[b]{b^{-1}}}} \)
First, simplify the nested radicals in the denominator:
\[
\sqrt[b]{\sqrt[b]{b^{-1}}} = b^{-\frac{1}{b^2}}
\]
Thus, the exponent becomes:
\[
\frac{b^b}{b^{-\frac{1}{b^2}}} = b^{b + \frac{1}{b^2}}
\]

### Step 4: Combine the expressions
Now substitute the simplified exponents back into the original expression:
\[
N = \left( \frac{1}{b^{b^{b^{-b^{-b}}}}} \right)^{b^{b + \frac{1}{b^2}}}
\]
This simplifies to:
\[
N = b^{-b^{(b + \frac{1}{b^2})} \cdot b^{b^{-b^{-b}}}}
\]
Since this is an exponent of a power, you multiply the exponents:
\[
N = b^{-b^{(b + \frac{1}{b^2} + b^{-b^{-b}})}}
\]

### Final Expression
So, the final simplified form of \(N\) is:
\[
N = b^{-b^{b + \frac{1}{b^2} + b^{-b^{-b}}}}
\]

This is a very compact way to write the expression without nested exponents.

Would you like more details, or do you have any questions? 

Here are five follow-up questions you might find interesting:
1. What is the general strategy for simplifying nested exponents?
2. How does the order of operations affect the simplification of exponents?
3. How can properties of logarithms be used to simplify similar expressions?
4. What are some real-world applications of such exponential expressions?
5. How do exponentiation and roots interact in complex numbers?

**Tip:** When dealing with nested exponents, start from the innermost part and work outward to simplify step by step.

Simplificar: N = (b^(-b^(b^(-b^(-b)))))^(b^b / (b^(-1/b))^(1/b))

Discover how to simplify a complex exponential expression involving nested exponents and radicals. Understand the properties of exponents and radicals to find the simplified form. Suitable for advanced mathematics students.

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