4-3/4b^5c^3 / -4/6b^2c^-3 =

four minus three fourths b to the 5th power c to the third power divided by negative four sixths b to the second power and c to the negative 2 power

To simplify the given expression:

1. Start by simplifying the fractional division: -4/6 = -2/3.
The expression becomes:

(4 - (3 / (4b^5c^3))) / (-2/3b^2c^-2)

2. Next, simplify the negative exponent in the denominator: c^-2 = 1 / c^2.
The expression becomes:

(4 - (3 / (4b^5c^3))) / (-2/3b^2c^2)

3. Now, to simplify further, we need to eliminate the fraction in the numerator: (3 / (4b^5c^3)).
To do this, multiply the numerator and denominator by the reciprocal of the fraction.
The expression becomes:

(4 - (3 * (4b^5c^3)^-1)) / (-2/3b^2c^2)

4. Simplify the exponent in the denominator: (4b^5c^3)^-1 = 1 / (4b^5c^3).
The expression becomes:

(4 - (3 / (4b^5c^3))) / (-2/3b^2c^2)

5. Distribute the negative sign in the denominator throughout the expression:
The expression becomes:

-(4 - (3 / (4b^5c^3))) / (2/3b^2c^2)

At this point, the expression is simplified as much as possible.