Sederhanakan bentuk berikut: (x^3)^(1/4).akar(x)...........

x^(38/9) * z^2 / y^2

Pembahasan

Untuk menyederhanakan bentuk (x^3)^(1/4) * akar(x) / (akar(x) / (x)^(1/3)))^(1/6) * (x^5 * y^2 * z^(-1) / (x^2 * y^4 / z^3)), kita perlu menerapkan sifat-sifat eksponen.

Langkah 1: Sederhanakan bagian pertama.
(x^3)^(1/4) * akar(x) = x^(3/4) * x^(1/2) = x^(3/4 + 2/4) = x^(5/4)

Langkah 2: Sederhanakan bagian kedua.
(akar(x) / (x)^(1/3)))^(1/6) = (x^(1/2) / x^(1/3)))^(1/6) = (x^(1/2 - 1/3)))^(1/6) = (x^(3/6 - 2/6)))^(1/6) = (x^(1/6)))^(1/6) = x^(1/36)

Langkah 3: Sederhanakan bagian ketiga.
(x^5 * y^2 * z^(-1) / (x^2 * y^4 / z^3)) = (x^(5-2) * y^(2-4) * z^(-1 - (-3))) = x^3 * y^(-2) * z^2 = (x^3 * z^2) / y^2

Langkah 4: Gabungkan semua bagian.
(x^(5/4) * (x^3 * z^2) / y^2) / x^(1/36)
= (x^(5/4 + 3) * z^2) / y^2 / x^(1/36)
= (x^(5/4 + 12/4) * z^2) / y^2 / x^(1/36)
= (x^(17/4) * z^2) / y^2 / x^(1/36)
= x^(17/4 - 1/36) * z^2 / y^2
= x^(153/36 - 1/36) * z^2 / y^2
= x^(152/36) * z^2 / y^2
= x^(38/9) * z^2 / y^2

Bentuk sederhana adalah x^(38/9) * z^2 / y^2