Sederhanakan operasi aljabar a. a^3 x 4ab^2 x (2b)^3 b.

a. 32a^4b^5, b. 4t^5m^3, c. 30x^9y^4

Pembahasan

Untuk menyederhanakan operasi aljabar tersebut, kita perlu menggunakan sifat-sifat eksponen:

a. a^3 x 4ab^2 x (2b)^3
   = a^3 x 4ab^2 x 8b^3
   = (1 x 4 x 8) x (a^3 x a) x (b^2 x b^3)
   = 32 x a^(3+1) x b^(2+3)
   = 32a^4b^5

b. (2tm)^2 x t^3 m
   = (2^2 x t^2 x m^2) x t^3 m
   = 4t^2m^2 x t^3m
   = 4 x (t^2 x t^3) x (m^2 x m)
   = 4 x t^(2+3) x m^(2+1)
   = 4t^5m^3

c. (2y^2) x 3(x^2 y)^2 x 5x^5
   = 2y^2 x 3(x^(2*2) y^2) x 5x^5
   = 2y^2 x 3x^4y^2 x 5x^5
   = (2 x 3 x 5) x (x^4 x x^5) x (y^2 x y^2)
   = 30 x x^(4+5) x y^(2+2)
   = 30x^9y^4