簡約 ((2^3)/3)^5*((3^2)/(2^5))^{-2}

解

簡約

(\frac{2 ^{3}}{3})^{5} \cdot (\frac{3 ^{2}}{2 ^{5}})^{- 2}

\frac{33554432}{19683}

十進法表記

1704.74175 \dots

解答ステップ

(\frac{2 ^{3}}{3})^{5} (\frac{3 ^{2}}{2 ^{5}})^{- 2}

(\frac{2 ^{3}}{3})^{5} = \frac{32768}{243}

= \frac{32768}{243} (\frac{3 ^{2}}{2 ^{5}})^{- 2}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

(\frac{3 ^{2}}{2 ^{5}})^{- 2} = \frac{1}{( \frac{3 ^{2}}{2 ^{5}} ) ^{2}}

= \frac{32768}{243} \cdot \frac{1}{( \frac{3 ^{2}}{2 ^{5}} ) ^{2}}

(\frac{3 ^{2}}{2 ^{5}})^{2} = \frac{81}{1024}

= \frac{32768}{243} \cdot \frac{1}{\frac{81}{1024}}

分数の規則を適用する:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{32768}{243} \cdot \frac{1024}{81}

\frac{32768}{243} \cdot \frac{1024}{81} = \frac{33554432}{19683}

= \frac{33554432}{19683}