簡約 ((1.9)/(1.3))^{1/4}-1

解

簡約

(\frac{1.9}{1.3})^{\frac{1}{4}} - 1

(\frac{19}{13})^{\frac{1}{4}} - 1

十進法表記

0.09951 \dots

解答ステップ

(\frac{1.9}{1.3})^{\frac{1}{4}} - 1

指数の規則を適用する:

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

(\frac{1.9}{1.3})^{\frac{1}{4}} = \frac{1. 9 ^{\frac{1}{4}}}{1. 3 ^{\frac{1}{4}}}

= \frac{1. 9 ^{\frac{1}{4}}}{1. 3 ^{\frac{1}{4}}} - 1

1.9 = \frac{19}{10}

= \frac{( \frac{19}{10} ) ^{\frac{1}{4}}}{1. 3 ^{\frac{1}{4}}} - 1

1.3 = \frac{13}{10}

= \frac{( \frac{19}{10} ) ^{\frac{1}{4}}}{( \frac{13}{10} ) ^{\frac{1}{4}}} - 1

\frac{( \frac{19}{10} ) ^{\frac{1}{4}}}{( \frac{13}{10} ) ^{\frac{1}{4}}} = (\frac{19}{13})^{\frac{1}{4}}

= (\frac{19}{13})^{\frac{1}{4}} - 1