簡約 (2x^{-1}y^2)^2

解

簡約

(2 x^{- 1} y^{2})^{2}

\frac{4 y ^{4}}{x ^{2}}

解答ステップ

(2 x^{- 1} y^{2})^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(2 x^{- 1} y^{2})^{2} = 2^{2} (x^{- 1})^{2} (y^{2})^{2}

= 2^{2} (x^{- 1})^{2} (y^{2})^{2}

2^{2} = 4

= 4 (x^{- 1})^{2} (y^{2})^{2}

簡素化

(x^{- 1})^{2} : \frac{1}{x ^{2}}

= 4 \cdot \frac{1}{x ^{2}} (y^{2})^{2}

簡素化

(y^{2})^{2} : y^{4}

= 4 \cdot \frac{1}{x ^{2}} y^{4}

簡素化

4 \cdot \frac{1}{x ^{2}} y^{4} : \frac{4 y ^{4}}{x ^{2}}

= \frac{4 y ^{4}}{x ^{2}}