簡約 ((9/2)^{10})/((4/9)^{10)}

解

簡約

\frac{( \frac{9}{2} ) ^{10}}{( \frac{4}{9} ) ^{10}}

\frac{9 ^{20}}{1073741824}

十進法表記

11322708296.642572

解答ステップ

\frac{( \frac{9}{2} ) ^{10}}{( \frac{4}{9} ) ^{10}}

(\frac{9}{2})^{10} = \frac{9 ^{10}}{1024}

= \frac{\frac{9 ^{10}}{1024}}{( \frac{4}{9} ) ^{10}}

(\frac{4}{9})^{10} = \frac{1048576}{9 ^{10}}

= \frac{\frac{9 ^{10}}{1024}}{\frac{1048576}{9 ^{10}}}

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{9 ^{10} \cdot 9 ^{10}}{1024 \cdot 1048576}

9^{10} \cdot 9^{10} = 9^{20}

= \frac{9 ^{20}}{1024 \cdot 1048576}

数を乗じる:

1024 \cdot 1048576 = 1073741824

= \frac{9 ^{20}}{1073741824}