Hitunglah! (1/25)^(1/4) x 5 akar(5) x 1/5 25^(1/4) x 25

5^(5/3)

Pembahasan

Untuk menghitung (1/25)^(1/4) x 5 akar(5) x 1/5 25^(1/4) x 25 625^(1/6), kita perlu menyederhanakan setiap bagian terlebih dahulu.
(1/25)^(1/4) = (1/5^2)^(1/4) = (5^-2)^(1/4) = 5^(-2/4) = 5^(-1/2) = 1/akar(5)
5 akar(5) = 5 * 5^(1/2) = 5^(3/2)
1/5 25^(1/4) = 1/5 * (5^2)^(1/4) = 1/5 * 5^(2/4) = 1/5 * 5^(1/2) = 5^(1/2) / 5 = 5^(-1/2) = 1/akar(5)
625^(1/6) = (5^4)^(1/6) = 5^(4/6) = 5^(2/3)
Jadi, ekspresi tersebut menjadi: (1/akar(5)) * 5^(3/2) * (1/akar(5)) * 5^(2/3)
= 5^(-1/2) * 5^(3/2) * 5^(-1/2) * 5^(2/3)
= 5^(-1/2 + 3/2 - 1/2 + 2/3)
= 5^(1 + 2/3)
= 5^(5/3)