[a^(3/2)/b^(1/2)]^-1 . [a^(3/2)b^(1/2)] :

a^(4/3)b^(1/2)

Pembahasan

Mari kita sederhanakan ekspresi matematika tersebut:

Ekspresi awal: [a^(3/2)/b^(1/2)]^-1 . [a^(3/2)b^(1/2)] : b^(1/2)/a^(1/3)}

Langkah 1: Sederhanakan bagian pertama.
[a^(3/2)/b^(1/2)]^-1 = b^(1/2)/a^(1/2)

Langkah 2: Ganti ekspresi yang disederhanakan ke dalam soal.
(b^(1/2)/a^(1/2)) . [a^(3/2)b^(1/2)] : b^(1/2)/a^(1/3)}

Langkah 3: Lakukan perkalian.
(b^(1/2)/a^(1/2)) * a^(3/2)b^(1/2) = (a^(3/2) * b^(1/2) * b^(1/2)) / a^(1/2)
= (a^(3/2) * b^1) / a^(1/2)
= a^(3/2 - 1/2) * b
= a^(2/2) * b
= a * b

Langkah 4: Lakukan pembagian.
(a * b) : (b^(1/2)/a^(1/3))
Ini sama dengan (a * b) * (a^(1/3)/b^(1/2))
= (a * b * a^(1/3)) / b^(1/2)

Langkah 5: Gabungkan basis yang sama.
= (a^(1 + 1/3) * b^1) / b^(1/2)
= (a^(4/3) * b^1) / b^(1/2)

Langkah 6: Sederhanakan bagian b.
= a^(4/3) * b^(1 - 1/2)
= a^(4/3) * b^(1/2)

Jadi, hasil penyederhanaannya adalah a^(4/3)b^(1/2).