https://file.aiquickdraw.com/mathbot/file/1730320578583ntyu1q73.jpg

negative and zero exponents— answer should contain only positive exponents

The expression given is:

\[
\frac{3yx^4}{6x^3}
\]

To simplify this and express the answer with only positive exponents, let’s break down each component:

### Step 1: Simplify the Coefficients
The coefficients \(3\) and \(6\) simplify as follows:
\[
\frac{3}{6} = \frac{1}{2}
\]

### Step 2: Simplify the \(x\) Terms Using Exponent Rules
The expression for \(x\) in the numerator and denominator is \(x^4\) and \(x^3\), respectively. Using the rule \(\frac{a^m}{a^n} = a^{m-n}\), we get:
\[
x^{4 - 3} = x^1 = x
\]

### Step 3: Combine the Results
After simplification, the expression becomes:
\[
\frac{1}{2} \cdot y \cdot x = \frac{yx}{2}
\]

### Final Answer
\[
\frac{yx}{2}
\]

Would you like a detailed explanation on any part of this simplification?

---

Here are 5 related questions to expand your understanding:
1. How would you simplify \(\frac{4x^5 y^2}{8x^3 y}\)?
2. What happens when there is a negative exponent in the denominator?
3. How do you handle variables in the numerator and denominator if they contain addition or subtraction?
4. Can you simplify an expression like \(\frac{5a^3b}{10a^2b^2}\)?
5. What if the exponents are zero in similar expressions?

**Tip:** Always reduce coefficients and simplify each variable separately when working with fractions involving exponents.

Simplify \(\frac{3yx^4}{6x^3}\) and express the answer with only positive exponents.

Learn how to simplify the expression \(\frac{3yx^4}{6x^3}\) with a step-by-step solution. This problem covers key algebraic concepts, including simplifying coefficients and using exponent rules. Suitable for students in 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