簡約 1000(0.5)^{70/30}

解

簡約

1000 (0.5)^{\frac{70}{30}}

2^{\frac{2}{3}} \cdot 125

十進法表記

198.42513 \dots

解答ステップ

1000 \cdot 0. 5^{\frac{70}{30}}

0.5 = \frac{1}{2}

= 1000 (\frac{1}{2})^{\frac{70}{30}}

共通因数を約分する:

10

= 1000 (\frac{1}{2})^{\frac{7}{3}}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{2})^{\frac{7}{3}} = \frac{1 ^{\frac{7}{3}}}{2 ^{\frac{7}{3}}}

= 1000 \cdot \frac{1 ^{\frac{7}{3}}}{2 ^{\frac{7}{3}}}

\frac{1 ^{\frac{7}{3}}}{2 ^{\frac{7}{3}}} = \frac{1}{4 \cdot 2 ^{\frac{1}{3}}}

= 1000 \cdot \frac{1}{4 \cdot 2 ^{\frac{1}{3}}}

1000 \cdot \frac{1}{4 \cdot 2 ^{\frac{1}{3}}} = 2^{\frac{2}{3}} \cdot 125

= 2^{\frac{2}{3}} \cdot 125