https://file.aiquickdraw.com/mathbot/file/1725423707507xjmrelf7.jpg

The expression shown in the image is:

\[
\frac{-24x^7 + 9x^3 - 15x}{3x^5}
\]

Let's simplify this expression by dividing each term in the numerator by the denominator \(3x^5\).

### Step-by-Step Simplification:

1. \(\frac{-24x^7}{3x^5} = -8x^{7-5} = -8x^2\)
2. \(\frac{9x^3}{3x^5} = 3x^{3-5} = 3x^{-2}\)
3. \(\frac{-15x}{3x^5} = -5x^{1-5} = -5x^{-4}\)

Now, combining all these terms, the simplified expression is:

\[
-8x^2 + 3x^{-2} - 5x^{-4}
\]

Would you like more details, or do you have any questions about this solution?

### Related Questions:
1. How do you simplify expressions with negative exponents?
2. How can this expression be rewritten with only positive exponents?
3. What are some common rules for dividing polynomials?
4. How do negative exponents affect the graph of a function?
5. Can this simplified expression be factored further?

### Tip:
Always carefully distribute the denominator when simplifying expressions to avoid mistakes.

Learn how to simplify the polynomial expression -24x^7 + 9x^3 - 15x over 3x^5 with a detailed step-by-step solution. This problem involves key algebraic concepts such as polynomial division and exponent rules. 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