簡約 (y/x)^2(3/(4xy))^3

解

簡約

(\frac{y}{x})^{2} (\frac{3}{4 x y})^{3}

\frac{27}{64 y x ^{5}}

解答ステップ

(\frac{y}{x})^{2} (\frac{3}{4 x y})^{3}

指数の規則を適用する:

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

(\frac{y}{x})^{2} = \frac{y ^{2}}{x ^{2}}

= \frac{y ^{2}}{x ^{2}} (\frac{3}{4 x y})^{3}

簡素化

(\frac{3}{4 x y})^{3} : \frac{27}{64 x ^{3} y ^{3}}

= \frac{y ^{2}}{x ^{2}} \cdot \frac{27}{64 x ^{3} y ^{3}}

分数の規則を適用する:

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

= \frac{y ^{2} \cdot 27}{x ^{2} \cdot 64 x ^{3} y ^{3}}

簡素化

\frac{y ^{2}}{y ^{3}} : \frac{1}{y}

= \frac{27}{x ^{2} \cdot 64 x ^{3} y}

簡素化

x^{2} x^{3} : x^{5}

= \frac{27}{x ^{5} \cdot 64 y}

= \frac{27}{64 x ^{5} y}

= \frac{27}{64 y x ^{5}}