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

the way you typed it , and the way you stated it,

I would multiply top and bottom by 12 to get rid of the fractions.

(48 - 9b5c3)/(-8b2c-3) or perhaps
(48c3 - 9b5c6)/-8b2

other than that I see little else that I would do

To simplify the expression, you need to follow the order of operations (also known as BODMAS or PEMDAS). Here's a step-by-step breakdown:

1. Simplify the numerator:
a. Determine the common denominator of 4 and 6, which is 12.
b. Rewrite 3/4b^5c^3 as (3b^5c^3)/(4) and multiply the numerator by 3 to get 3b^5c^3.
c. Rewrite -4/6b^2c^-3 as (-4b^2c^-3)/(6) and multiply the numerator by -4 to get -4b^2c^-3.
d. Combine the numerators: 3b^5c^3 - 4b^2c^-3.

2. Simplify the denominator:
a. Multiply -4/6b^2c^-3 by -2/2 to change the denominator from 6 to 12. This gives (-4b^2c^-3 * -2)/(12).
b. Simplify -4 * -2 to 8, resulting in 8b^2c^-3/12.

3. Combine the simplified numerator and denominator:
(3b^5c^3 - 4b^2c^-3) / (8b^2c^-3/12).

4. Simplify the expression even further by multiplying the numerator by the reciprocal of the denominator:

(3b^5c^3 - 4b^2c^-3) * (12/8b^2c^-3).

5. Simplify further by canceling out like terms:
- The b^2 in the numerator cancels out with b^2 in the denominator.
- The c^-3 in the numerator cancels out with c^-3 in the denominator.

After canceling out those terms, you are left with:

(3b^3c^6)/(2)

So, the simplified expression is (3b^3c^6)/(2).