[Risolto] Richiesta risoluzione espressione

Calcoliamo il numeratore:

(144^2/24^3)^8/(- (- 2/3)^3)^(-3)=

=(2^8·3^4/(2^9·3^3))^8/(2^3/3^3)^(-3)=

=(3/2)^8/(2^3/3^3)^(-3)=

=3^8/2^8/(3^9/2^9)=

=3^8/2^8·(2^9/3^9)=2/3

Calcoliamo il denominatore:

((83 - 8)/90)^10·(- 8/10)^10/(- (- 6/9)^4)^3 =

=(5/6)^10·(- 2^2/5)^10/(- 2^4/3^4)^3=

=(5/6)^10·(- 2^2/5)^10/(- 2^12/3^12)=

=(5/6)^10·(2^20/5^10)/(- 2^12/3^12)=

=5^10/(2^10·3^10)·(2^20/5^10)/(- 2^12/3^12)=

=2^10/3^10/(- 2^12/3^12)=

=2^10/3^10·(- 3^12/2^12)=

=- 3^2/2^2 = - 9/4

Quindi la frazione assegnata vale:

2/3·(- 4/9) = - 8/27