Question

How do you evaluate `\frac { - 4} { 3} \times ( \frac { 6} { - 5} \times \frac { 8} { 9} ) = [ \frac { 4} { - 3} \times ( \frac { 6} { - 5} ) ] \times \frac { 8} { 9}`?

Answer 1

I am assuming that you are simply trying to verify the associative property for multiplication for this equation by evaluating the Left and Right sides separately and showing they are equal.
(see below).

Explanation:

#{: ("Left side:",color(white)("xxx"),"Right side:"), (=(-4)/3xx(6/(-5)xx8/9),,=[4/(-3)xx(6/(-5))]xx8/9), (=(-4)/3xx(2xx8)/(-5xx3),,=[(4xx2)/(-1xx-5)]xx8/9), (=(-4)/3xx16/(-15),,=[8/5]xx8/9), (=64/45,,=64/45), (color(blue)("Left side"),color(red)(=),color(blue)("Right side")) :}#