We will simplify the given expression step by step:

$\left( \frac{1}{5} \right)^2 \cdot \left( \frac{1}{5} \right)^{-4} \cdot \left( \frac{1}{5} \right)^3$

Step 1: Use the property of exponents

When multiplying terms with the same base, we can add the exponents. The base here is $\frac{1}{5}$.

So the exponents become: $2 + (-4) + 3$

Step 2: Simplify the exponents

$2 + (-4) + 3 = 1$

Step 3: Rewrite the expression

The expression simplifies to: $\left( \frac{1}{5} \right)^1 = \frac{1}{5}$

So, the simplified result is: $\boxed{\frac{1}{5}}$

Would you like more details on exponent rules or have any other questions?

Here are some related questions you might explore:

1. What happens when you multiply powers with negative exponents?
2. How does the exponent rule $a^m \cdot a^n = a^{m+n}$ apply in general?
3. How do you simplify expressions with fractional bases and exponents?
4. What is the difference between positive and negative exponents?
5. How do you handle division with exponents in expressions?

Tip: Always simplify the exponents first when multiplying terms with the same base.