https://file.aiquickdraw.com/mathbot/file/1726879747141e5pi82lp.jpg

Let's simplify the given expression step by step.

The expression is:

\[
\frac{16x^2 y^7}{40x^8 y^3}
\]

### Step 1: Simplify the numerical coefficients
Simplify the fraction \(\frac{16}{40}\):
\[
\frac{16}{40} = \frac{4}{10} = \frac{2}{5}
\]

### Step 2: Simplify the \(x\)-terms
For the \(x\)-terms, use the rule \(\frac{x^a}{x^b} = x^{a-b}\):
\[
\frac{x^2}{x^8} = x^{2-8} = x^{-6}
\]

Since we only want positive exponents, we can write \(x^{-6} = \frac{1}{x^6}\).

### Step 3: Simplify the \(y\)-terms
For the \(y\)-terms, similarly use the rule \(\frac{y^a}{y^b} = y^{a-b}\):
\[
\frac{y^7}{y^3} = y^{7-3} = y^4
\]

### Step 4: Combine the results
Now put everything together:
\[
\frac{2}{5} \cdot \frac{y^4}{x^6} = \frac{2y^4}{5x^6}
\]

### Final Answer:
\[
\frac{2y^4}{5x^6}
\]

This is the fully simplified expression with only positive exponents.

Would you like further explanation or details on any step?

Here are 5 related questions to expand your understanding:
1. How do you handle negative exponents when simplifying?
2. Can you explain how to simplify other algebraic fractions involving exponents?
3. What are the rules for multiplying and dividing powers with the same base?
4. How do you simplify an expression with variables raised to powers outside of fractions?
5. How does the result change if there are more variables or higher powers in the original fraction?

**Tip**: Always simplify the numerical coefficients first, then handle the variables by applying exponent rules.

Fully simplify using only positive exponents: (16x^2 y^7) / (40x^8 y^3)

Simplify the algebraic expression (16x^2 y^7) / (40x^8 y^3) using exponent laws and positive exponents. Learn how to reduce numerical coefficients and apply exponent rules to variables for full simplification. 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