https://file.aiquickdraw.com/mathbot/file/172649507251516cmp1eg.jpg

The given expression is:

\[
\frac{n^{-2} m}{7 m^{-4} n^{-3}}
\]

To simplify this, we'll follow these steps:

1. **Simplify the powers of \( n \):**
   \[
   \frac{n^{-2}}{n^{-3}} = n^{-2 - (-3)} = n^{-2 + 3} = n^{1}
   \]
   So, the powers of \( n \) simplify to \( n \).

2. **Simplify the powers of \( m \):**
   \[
   \frac{m}{m^{-4}} = m^{1 - (-4)} = m^{1 + 4} = m^{5}
   \]
   So, the powers of \( m \) simplify to \( m^5 \).

3. **Combine with the constant \( 7 \):**
   The constant in the denominator is \( 7 \), so the simplified expression becomes:

   \[
   \frac{n m^5}{7}
   \]

Thus, the simplified expression is:

\[
\frac{n m^5}{7}
\]

Would you like further details or have any questions?

---

Here are 5 related questions for practice:
1. How do you simplify \(\frac{x^{-3}y}{5x^{-5}y^{-2}}\)?
2. What are the rules for simplifying expressions with negative exponents?
3. How can you rewrite the expression \(\frac{a^2b^{-3}}{4b^5a^{-1}}\) in simplified form?
4. What happens when both the numerator and denominator have negative powers of the same variable?
5. How do you apply exponent rules when dividing variables with different bases?

**Tip:** When simplifying expressions with exponents, always apply the power rules carefully to each base separately before combining terms!

Simplify the expression: (n^(-2) * m) / (7 * m^(-4) * n^(-3))

Learn how to simplify the algebraic expression (n^(-2) * m) / (7 * m^(-4) * n^(-3)) using exponent rules. This step-by-step guide covers key concepts, including simplifying powers of variables and constants. 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