To solve the given expression:

$\frac{x^{-5} \cdot x^3}{x^{-2}}$

Step 1: Simplify the numerator

Using the property of exponents $x^a \cdot x^b = x^{a+b}$:

$x^{-5} \cdot x^3 = x^{-5+3} = x^{-2}.$

So, the numerator simplifies to $x^{-2}$.

Step 2: Simplify the fraction

The entire expression becomes:

$\frac{x^{-2}}{x^{-2}}.$

Using the property of exponents $\frac{x^a}{x^b} = x^{a-b}$:

$x^{-2-(-2)} = x^{0}.$

Step 3: Simplify $x^0$

Any number (except 0) raised to the power of 0 equals 1. Thus:

$x^0 = 1.$

Final Answer:

$\boxed{1}$

Would you like further clarification or details on this solution?

Here are 5 related questions to expand your understanding:

1. What happens if the exponents in the numerator and denominator differ?
2. How do the properties of exponents apply to division?
3. What is the value of $x^0$ if $x = 0$?
4. How do negative exponents influence the calculation?
5. Can you simplify similar expressions with fractional exponents?

Tip: Always simplify step-by-step and use the rules of exponents systematically.