Jika a = -3, b = 2 dan c = 1/4, tentukan hasil operasi

a. 9/2, b. -48, c. 16384/9, d. 13/2048

Pembahasan

Diketahui:
a = -3
b = 2
c = 1/4

a. a^2bc
a^2bc = (-3)^2 * (2) * (1/4)
= (9) * (2) * (1/4)
= 18 * (1/4)
= 18/4
= 9/2

b. 8ab^-3c^-2
8ab^-3c^-2 = 8 * (-3) * (2)^-3 * (1/4)^-2
= -24 * (1/2^3) * (4^2)
= -24 * (1/8) * (16)
= -3 * 16
= -48

c. (ab^4c^-3)/(a^3b^-2c)
(ab^4c^-3)/(a^3b^-2c) = ((-3) * (2^4) * (1/4)^-3) / ((-3)^3 * (2^-2) * (1/4))
= ((-3) * 16 * 4^3) / (-27 * (1/4) * (1/4))
= ((-3) * 16 * 64) / (-27 * 1/16)
= (-3072) / (-27/16)
= -3072 * (-16/27)
= 3072 * 16 / 27
= 49152 / 27
= 1820.44...
Mari kita hitung ulang dengan menyederhanakan terlebih dahulu:
(a^(1-3)) * (b^(4-(-2))) * (c^(-3-1))
= a^-2 * b^6 * c^-4
= (1/a^2) * b^6 * (1/c^4)
= b^6 / (a^2 * c^4)
= (2^6) / ((-3)^2 * (1/4)^4)
= 64 / (9 * (1/256))
= 64 / (9/256)
= 64 * (256/9)
= 16384 / 9
= 1820.44...
Saya akan gunakan hasil penyederhanaan untuk jawaban yang lebih tepat.
16384 / 9

d. (ab^-1c^-1 + a^2bc^2)/(ab^2c^-3)
Langkah 1: Hitung pembilang (ab^-1c^-1 + a^2bc^2)
ab^-1c^-1 = (-3)(2^-1)(1/4)^-1 = (-3)(1/2)(4) = -6
a^2bc^2 = (-3)^2(2)(1/4)^2 = 9(2)(1/16) = 18/16 = 9/8
Pembilang = -6 + 9/8 = -48/8 + 9/8 = -39/8

Langkah 2: Hitung penyebut (ab^2c^-3)
ab^2c^-3 = (-3)(2^2)(1/4)^-3 = (-3)(4)(4^3) = (-3)(4)(64) = -12 * 64 = -768

Langkah 3: Bagi pembilang dengan penyebut
(-39/8) / (-768)
= (-39/8) * (-1/768)
= 39 / (8 * 768)
= 39 / 6144
= 13 / 2048

Jadi:
a. a^2bc = 9/2
b. 8ab^-3c^-2 = -48
c. (ab^4c^-3)/(a^3b^-2c) = 16384/9
d. (ab^-1c^-1 + a^2bc^2)/(ab^2c^-3) = 13/2048