The expression given in the image is:

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

Step-by-step simplification:

1. Apply the rule of exponents: When dividing terms with the same base, you subtract the exponents. In this case, the base is $x$, so we subtract the exponents: $-x^{-3} \div x^2 = -x^{-3-2} = -x^{-5}$

2. Simplify: The result is: $-x^{-5}$

3. Express with positive exponents: We can rewrite the negative exponent as a reciprocal: $-x^{-5} = -\frac{1}{x^5}$

Final Answer:

$-\frac{1}{x^5}$

Would you like further details or have any questions about this problem?

Related questions:

1. How would you simplify $\frac{x^3}{x^{-2}}$?
2. What is the value of $\frac{-x^{-3}}{x^4}$?
3. Can you simplify $\frac{x^{-5}}{x^{-1}}$?
4. How would you simplify $\frac{x^2}{-x^{-3}}$?
5. What is the simplified result of $\frac{-2x^{-3}}{4x^2}$?

Tip:

Always remember that when dividing like bases, subtract the exponents: $\frac{x^a}{x^b} = x^{a-b}$.