 | ■No9397に返信(ひなたさんの記事)
> (1) ([4]√3)[8]=9
> (2) ([3]√-2)9=-8
> (3) [3]√54+[3]√16=5[3]√2
> (5) 10[-1]=1/10
> (6) (0.1)[-2]=-8
> (7) 32[-1/5]=5[3]√2
> (8) (25[3])[1/2]=125
> (9) (49[-2/3])[3/4]=1/7
(1) ([4]√3)[8]=3^{(1/4)8}=3^2=9
(2) ([3]√-2)9=(-2)^{(1/3)9}=(-2)^3=-8
(3) [3]√54+[3]√16=54^(1/3)+16^(1/3)=(23^3)^(1/3)+(2^4)^(1/3)=3*3^(1/3)+2*2^(1/3)=(3+2)2^(1/3)=5[3]√2
(5) 10[-1]=10^(-1)=1/10
(6) (0.1)[-2]=10^{(-1)(-2)}=10^2=100
(7) 32[-1/5]=(2^5)^(-1/5)=2^(-1)=1/2
(8) (25[3])[1/2]={(5^2)^3}^(1/2)=5^3=125
(9) (49[-2/3])[3/4]=7^{2(-2/3)(3/4)}=7^(-1)=1/7
「*」は「掛ける」の意。(6)(7)が違うと思いますが？(4)はどこへ？
|