## To simplify the expression (7m^7n^4/8m) / (9m^2n^9/5n^2), you can follow these steps:

1. Start by simplifying each fraction separately.

- In the numerator (7m^7n^4), all the m terms and n terms are already together, so it remains as it is.

- In the denominator (8m), the m term is alone, so it remains as it is.

2. Now, divide the two fractions by dividing the numerator of the first fraction by the denominator of the second fraction. Similarly, divide the denominator of the first fraction by the numerator of the second fraction.

Numerator:

(7m^7n^4) / (8m) = 7n^4 / 8

Denominator:

(9m^2n^9) / (5n^2) = 9m^2 / 5

3. Finally, simplify the resulting expression by combining like terms.

The simplified expression becomes:

(7n^4 / 8) / (9m^2 / 5) = (7 * 5 * n^4) / (8 * 9 * m^2) = 35n^4 / 72m^2

Therefore, the correct simplification of the initial expression is:

35n^4 / 72m^2