簡約 (-4b^{-5}c^2)^2

解

簡約

(- 4 b^{- 5} c^{2})^{2}

\frac{16 c ^{4}}{b ^{10}}

解答ステップ

(- 4 b^{- 5} c^{2})^{2}

指数の規則を適用する:

(- a)^{n} = a^{n},

(

n

が偶数の場合)

(- 4 b^{- 5} c^{2})^{2} = (4 b^{- 5} c^{2})^{2}

= (4 b^{- 5} c^{2})^{2}

指数の規則を適用する:

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

(4 b^{- 5} c^{2})^{2} = 4^{2} (b^{- 5})^{2} (c^{2})^{2}

= 4^{2} (b^{- 5})^{2} (c^{2})^{2}

4^{2} = 16

= 16 (b^{- 5})^{2} (c^{2})^{2}

簡素化

(b^{- 5})^{2} : \frac{1}{b ^{10}}

= 16 \cdot \frac{1}{b ^{10}} (c^{2})^{2}

簡素化

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

= 16 \cdot \frac{1}{b ^{10}} c^{4}

簡素化

16 \cdot \frac{1}{b ^{10}} c^{4} : \frac{16 c ^{4}}{b ^{10}}

= \frac{16 c ^{4}}{b ^{10}}