Nyatakan hasil operasi berikut dalam bentuk yang paling

a. a^2 * b^(4/5), b. a^(2/3) / b^(1/2)

Pembahasan

Untuk menyederhanakan bentuk aljabar:
a. (a^(1/2)xb^(-1/3)/b^(2/3)xa^3)^-4/5
= (a^(1/2 - 3) * b^(-1/3 - 2/3))^-4/5
= (a^(-5/2) * b^(-1))^-4/5
= a^(-5/2 * -4/5) * b^(-1 * -4/5)
= a^2 * b^(4/5)
b. (a^(2/3)/b^(1/2))^-1x(a^(1/3)b^(-1/2))^3:(b^(1/2)/a^(1/3))
= (a^(-2/3) * b^(1/2)) * (a^(1/3*3) * b^(-1/2*3)) : (b^(1/2) * a^(-1/3))
= (a^(-2/3) * b^(1/2)) * (a^1 * b^(-3/2)) : (b^(1/2) * a^(-1/3))
= a^(-2/3 + 1 - (-1/3)) * b^(1/2 - 3/2 - 1/2)
= a^(-2/3 + 1 + 1/3) * b^(-1/2)
= a^(2/3) * b^(-1/2)
= a^(2/3) / b^(1/2)

Jadi, hasil penyederhanaannya adalah:
a. a^2 * b^(4/5)
b. a^(2/3) / b^(1/2)