https://file.aiquickdraw.com/mathbot/file/1730124308228f6swa6vt.jpg

The image contains three algebraic expressions to simplify. Let's go through each one step by step.

### 1. Simplify

#### Part (a)
\[
\frac{x^5 y^8}{x^3 y}
\]

To simplify:
1. Apply the quotient rule for exponents: \(\frac{x^m}{x^n} = x^{m-n}\).
2. Separate \(x\) and \(y\) terms:

   \[
   = x^{5 - 3} y^{8 - 1} = x^2 y^7
   \]

**Answer:** \( x^2 y^7 \)

#### Part (b)
\[
2(2x + y - 7)
\]

To simplify:
1. Distribute \(2\) across each term inside the parentheses:

   \[
   = 2 \cdot 2x + 2 \cdot y - 2 \cdot 7
   \]
   \[
   = 4x + 2y - 14
   \]

**Answer:** \( 4x + 2y - 14 \)

#### Part (c)
\[
4x^2(3 - x^3) - 2x(5x - x^2)
\]

To simplify:
1. Distribute \(4x^2\) across the terms in the first part and \(-2x\) in the second part:

   \[
   = 4x^2 \cdot 3 - 4x^2 \cdot x^3 - 2x \cdot 5x + 2x \cdot x^2
   \]
   \[
   = 12x^2 - 4x^5 - 10x^2 + 2x^3
   \]

2. Combine like terms:

   \[
   = (12x^2 - 10x^2) - 4x^5 + 2x^3
   \]
   \[
   = 2x^2 - 4x^5 + 2x^3
   \]

**Answer:** \( 2x^2 - 4x^5 + 2x^3 \)

---

Would you like more details on any part or have questions?

### Related Questions

1. How does the quotient rule for exponents work in other contexts?
2. What is the distributive property, and how is it used in algebra?
3. Can you factorize expressions similar to these?
4. How would these simplifications change if there were negative exponents?
5. What are other rules of exponents, and how do they help simplify expressions?

### Tip
Always combine like terms at the end to ensure the expression is in its simplest form.

Simplify the algebraic expressions: (a) x^5 * y^8 / x^3 * y, (b) 2(2x + y - 7), and (c) 4x^2(3 - x^3) - 2x(5x - x^2).

Step-by-step guide on simplifying algebraic expressions involving exponents and distribution. Includes examples like x^5 * y^8 / x^3 * y, 2(2x + y - 7), and 4x^2(3 - x^3) - 2x(5x - x^2). Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation