簡約 ((3/2)^{10})/((4/3)^{10)}

解

簡約

\frac{( \frac{3}{2} ) ^{10}}{( \frac{4}{3} ) ^{10}}

\frac{3486784401}{1073741824}

十進法表記

3.24732 \dots

解答ステップ

\frac{( \frac{3}{2} ) ^{10}}{( \frac{4}{3} ) ^{10}}

(\frac{3}{2})^{10} = \frac{59049}{1024}

= \frac{\frac{59049}{1024}}{( \frac{4}{3} ) ^{10}}

(\frac{4}{3})^{10} = \frac{1048576}{59049}

= \frac{\frac{59049}{1024}}{\frac{1048576}{59049}}

分数の規則を適用する:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{59049 \cdot 59049}{1024 \cdot 1048576}

数を乗じる:

59049 \cdot 59049 = 3486784401

= \frac{3486784401}{1024 \cdot 1048576}

数を乗じる:

1024 \cdot 1048576 = 1073741824

= \frac{3486784401}{1073741824}