https://file.aiquickdraw.com/mathbot/file/1725415416183apdet5c8.jpg

The expression in the image appears to be:

\[
\frac{5x^2 \cdot x^{-2} \cdot x^3}{x^{10}}
\]

### Let's simplify this step by step:

1. **Combine the exponents in the numerator:**
   - \(x^2 \cdot x^{-2} \cdot x^3\) 
   - Using the property \(x^a \cdot x^b = x^{a+b}\), we get:
     \[
     x^{2 + (-2) + 3} = x^{3}
     \]
   - So the numerator simplifies to \(5x^3\).

2. **Now divide by the denominator:**
   - \(\frac{5x^3}{x^{10}}\)
   - Using the property \(\frac{x^a}{x^b} = x^{a-b}\), we get:
     \[
     5x^{3 - 10} = 5x^{-7}
     \]

### Final simplified expression:

\[
\boxed{5x^{-7}}
\]

This is the final simplified form of the given expression.

Would you like more details or have any questions? 

Here are some related questions to deepen your understanding:

1. What is the general rule for combining exponents when multiplying terms with the same base?
2. How do you handle exponents when dividing terms with the same base?
3. Can you convert \(5x^{-7}\) into a fraction with a positive exponent?
4. How would the expression change if the denominator was \(x^{-10}\) instead of \(x^{10}\)?
5. What are the applications of manipulating exponents in more complex algebraic expressions?

**Tip:** When working with exponents, always keep in mind the basic rules of adding and subtracting exponents during multiplication and division, respectively. This will help in simplifying expressions efficiently.

Simplify the expression: 5x^2 * x^(-2) * x^3 / x^10

Learn how to simplify the expression 5x^2 * x^(-2) * x^3 / x^10 by combining and dividing exponents. This algebraic problem is suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation