7m              10m
-----   .    ---------
m^5            14wn^3

The given expression is:

\[
\frac{7m}{m^5} \cdot \frac{10m}{14wn^3}
\]

Let's simplify this step by step.

### Step 1: Simplify the first fraction
\[
\frac{7m}{m^5} = \frac{7}{m^4}
\]
(Since \( m^5 \div m = m^4 \)).

### Step 2: Simplify the second fraction
\[
\frac{10m}{14wn^3} = \frac{5m}{7wn^3}
\]
(Simplify \( 10 \div 14 \) to \( 5 \div 7 \)).

### Step 3: Multiply the two simplified fractions
\[
\frac{7}{m^4} \cdot \frac{5m}{7wn^3}
\]
The \( 7 \)'s cancel out, and we're left with:
\[
\frac{5m}{m^4 \cdot wn^3}
\]

### Step 4: Simplify the remaining expression
\[
\frac{5m}{m^4 \cdot wn^3} = \frac{5}{m^3 \cdot wn^3}
\]
(Since \( m \div m^4 = m^{-3} \)).

### Final Answer:
\[
\frac{5}{m^3 \cdot wn^3}
\]

This is the fully simplified expression.

Would you like further clarification or details?

Here are 5 related questions you might find helpful:
1. How do you simplify expressions with exponents in division?
2. How do you handle variables when multiplying fractions?
3. What rules apply when simplifying expressions with different variables?
4. How do you apply exponent rules to simplify complex expressions?
5. How do you factor expressions that contain multiple variables?

**Tip:** Always reduce numerical coefficients first before simplifying variables to avoid mistakes!

Simplify the algebraic expression 7m / m^5 * 10m / 14wn^3 step by step. This problem involves exponent rules, fraction simplification, and variable manipulation. Suitable for students in Grades 9-11.

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