簡約 (1/3)^3(3/10)^3(5/7)^3

解

簡約

(\frac{1}{3})^{3} \cdot (\frac{3}{10})^{3} \cdot (\frac{5}{7})^{3}

\frac{1}{2744}

十進法表記

0.00036 \dots

解答ステップ

(\frac{1}{3})^{3} (\frac{3}{10})^{3} (\frac{5}{7})^{3}

(\frac{1}{3})^{3} = \frac{1}{27}

= \frac{1}{27} (\frac{3}{10})^{3} (\frac{5}{7})^{3}

(\frac{3}{10})^{3} = \frac{27}{1000}

= \frac{1}{27} \cdot \frac{27}{1000} (\frac{5}{7})^{3}

指数の規則を適用する:

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

(\frac{5}{7})^{3} = \frac{5 ^{3}}{7 ^{3}}

= \frac{1}{27} \cdot \frac{27}{1000} \cdot \frac{5 ^{3}}{7 ^{3}}

5^{3} = 125

= \frac{1}{27} \cdot \frac{27}{1000} \cdot \frac{125}{7 ^{3}}

7^{3} = 343

= \frac{1}{27} \cdot \frac{27}{1000} \cdot \frac{125}{343}

共通因数をクロス約分する:

27

= \frac{1}{1000} \cdot \frac{125}{343}

\frac{1}{1000} \cdot \frac{125}{343} = \frac{1}{2744}

= \frac{1}{2744}