To divide rational numbers, we need to multiply the first number by the reciprocal of the second number.

First, let’s simplify the expression inside the parentheses: (-45)/48 = -45/48

Now, let’s find the reciprocal of (125/64): Reciprocal of (125/64) = (64/125)

Now, we can rewrite the expression as: 100/-254 ÷ (125/64 ÷ (-45)/48) = 100/-254 * (64/125) * (48/-45)

Next, let’s simplify each fraction: 100/-254 = -50/127 64/125 = 64/125 48/-45 = -16/15

Now, we can rewrite the expression as: (-50/127) * (64/125) * (-16/15)

To multiply fractions, we multiply the numerators together and the denominators together: (-50 * 64 * -16) / (127 * 125 * 15)

Simplifying the numerator and denominator: (51200) / (238875)

Therefore, the simplified expression is 51200/238875.