The problem asks to find the value of:

$\left( \frac{1}{3-2} \right)^{-3}$

Step-by-Step Solution:

1. Simplify the denominator:
   $3 - 2 = 1$

   Now the expression becomes:

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

2. Simplify the fraction:
   $\frac{1}{1} = 1$

   So the expression simplifies to:

   $1^{-3}$

3. Evaluate the exponent:
   Any number raised to any power will result in that number, so:

   $1^{-3} = 1$

Thus, the value of the expression is 1.

Would you like any more details on this?

Here are five related questions:

1. What is the result when a negative exponent is applied to a number?
2. How do you simplify expressions with exponents?
3. Can a fraction raised to a negative power ever result in a negative number?
4. How does changing the denominator in the original fraction affect the final result?
5. What are the general rules for evaluating expressions with zero exponents?

Tip: Remember that any number raised to the power of 0 is always 1, and $1$ raised to any power remains $1$!