https://file.aiquickdraw.com/mathbot/file/1726529670698wayj32vm.jpg

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: \( \frac{x^a}{x^b} = x^{a-b} \).

Learn how to simplify algebraic expressions with exponents by using exponent subtraction rules. This example simplifies -x^{-3}/x^2 to -1/x^5, covering exponent rules and negative exponents. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation