https://file.aiquickdraw.com/mathbot/file/1726862198679oozi1yl4.jpg

Let's simplify the expression:

\[
\frac{125x^5y^4}{5x^8y^6}
\]

### Step 1: Simplify the coefficients
\[
\frac{125}{5} = 25
\]

### Step 2: Simplify the powers of \(x\)
Using the law of exponents \(\frac{x^m}{x^n} = x^{m-n}\):
\[
\frac{x^5}{x^8} = x^{5-8} = x^{-3}
\]

### Step 3: Simplify the powers of \(y\)
\[
\frac{y^4}{y^6} = y^{4-6} = y^{-2}
\]

### Step 4: Combine everything
Now we have:
\[
25x^{-3}y^{-2}
\]

Since the problem specifies that only positive exponents are allowed, rewrite the expression with positive exponents by moving the terms with negative exponents to the denominator:
\[
\frac{25}{x^3y^2}
\]

### Final Answer:
\[
\frac{25}{x^3y^2}
\]

Would you like further details on any step? Here are five related questions to explore:

1. What is the rule for simplifying expressions with exponents in fractions?
2. How do you handle negative exponents when simplifying?
3. Can the process be applied to more complex expressions involving radicals and exponents?
4. What other exponent laws might be useful for different types of algebraic simplifications?
5. How do these exponent rules extend to logarithmic functions?

**Tip:** Always check if you can simplify coefficients and variables separately when working with fractions involving exponents.

Fully simplify using only positive exponents: 125x^5y^4 / 5x^8y^6

Learn how to fully simplify the algebraic expression 125x^5y^4 / 5x^8y^6 using positive exponents. This step-by-step guide covers exponent rules and coefficient simplifications, 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