Kelas 9mathAljabar
Jika a = -3, b = 2 dan c = 1/4, tentukan hasil operasi
Pertanyaan
Jika a = -3, b = 2 dan c = 1/4, tentukan hasil operasi berikut! a. a^2b^3c b. 8ab^-3c^-2 c. (ab^4c^-3)/(a^3b^-2c) d. (ab^-1c^-1 + a^2bc^2)/(ab^2c^-3)
Solusi
Verified
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
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Topik: Bilangan Pangkat
Section: Operasi Bilangan Pangkat
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