To simplify the expression $\frac{10 m^2 n^4}{16 m^6 n^2}$ with positive exponents, follow these steps:

Step 1: Simplify the coefficients

$\frac{10}{16} = \frac{5}{8}$

Step 2: Simplify the $m$ terms

$\frac{m^2}{m^6} = m^{2-6} = m^{-4}$

Step 3: Simplify the $n$ terms

$\frac{n^4}{n^2} = n^{4-2} = n^2$

Step 4: Combine the simplified terms

$\frac{5}{8} \cdot m^{-4} \cdot n^2 = \frac{5 n^2}{8 m^4}$

Final Answer

$\frac{10 m^2 n^4}{16 m^6 n^2} = \frac{5 n^2}{8 m^4}$

Would you like more details on this solution or have any questions?

Here are 5 related questions you might find useful:

1. How do you simplify expressions with negative exponents?
2. What are the properties of exponents used in division?
3. How do you convert a negative exponent to a positive one?
4. What is the general rule for simplifying fractional exponents?
5. How do you simplify algebraic fractions with multiple variables?

Tip: When dividing like bases with exponents, subtract the exponents of the denominator from those of the numerator.