Sederhanakan bentuk akar berikut ini. c. ((p^(5)q^(−10))/(p^(5)q^(−4)))^(1/2)((p^(1/4)q^(−1/2))/(p^(−1/2)q^(−1/2)))^(1/2)

Jawabnya adalah p^(3/8) / q^(3) Ingat (a/b)^m = a^m / b^m (a^m)^n = a^(mn) a^m : a^n = a^(m-n) a^m. a^n = a^(m+n) a^(-m) = 1/(a^m) ((p^(5)q^(−10))/(p^(5)q^(−4)))^(1/2)((p^(1/4)q^(−1/2))/(p^(−1/2)q^(−1/2)))^(1/2) = ((p^(5)q^(−10))^(1/2)/(p^(5)q^(−4))^(1/2))((p^(1/4)q^(−1/2))^(1/2)/(p^(−1/2)q^(−1/2))^(1/2)) = ((p^(5/2)q^(−5))/(p^(5/2)q^(−2)))((p^(1/8)q^(−1/4))/(p^(−1/4)q^(−1/4)) = (p^(5/2-5/2) q^(-5-(-2)))(p^(1/8-(-1/4) q^(-1/4 -(-1/4))) = (p^(0) q^(-3))(p^(3/8) q^(0)) = p^(0+3/8) q^(-3+0) = p^(3/8) q^(-3) = p^(3/8) / q^(3) Jadi Jawabnya adalah p^(3/8) / q^(3)