12^(1/2) =4^(1/2)*3^(1/2) =(2²)^1/2 *3^1/2 =2 *3^(1/2)
8^(1/2) =4^(1/2)*2^(1/2) =(2²)^1/2 *2^(1/2)=2*2^(1/2)
8^(1/6) =(2²)^1/6 *2^(1/6) =2^(1/3) *2^(1/6) =2^(1/3+1/6) =2^(3/6) =2^(1/2)
7^(5/3) : 7^(2/3) =7^(5/3 -2/3) =7^(3/3) =7
числитель:
(2*3^(1/2) *3^(1/2)*7 =2 *3^(1/2 +1/2) *7 =14*3^(2/2) =14*3 =42
знаменатель:
2*2^(1/2) *2^(1/2) =2 *2^(1/2 +1/2) =2 *2^(2/2) =2*2 =4
=42/4 =10.5
ответ: 10.5
2. 12^(1/3) *6^(2/3) *(0.5)^1/3 =2^(1/3) *6^(1/3) *6^(2/3) *(1/2)^1/3 =2^(1/3) /2^(1/3) *6^(1/3 +2/3) =1 *6^(3/3) =1*6 =6
(2^(1/3) *(1/2)^1/3 =2^(1/3) /2^(1/3) =1)
ответ: 6
3. =a^(9/2 -19/4) *b^(1/12 -1/3) =a^(18-19)/4) *b^(1-4)/12) =a^(-1/4) *b^(-3/12) =a^(-1/4) *b^(-1/4) =(ab)^(-1/4) =(1/ab)^1/4
ответ: (1/ab)^(1/4)
значок ^ обозначает в степени