簡約 (-4a^2b^{-7}c)^2

解

簡約

(- 4 a^{2} b^{- 7} c)^{2}

\frac{16 a ^{4} c ^{2}}{b ^{14}}

解答ステップ

(- 4 a^{2} b^{- 7} c)^{2}

指数の規則を適用する:

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

(

n

が偶数の場合)

(- 4 a^{2} b^{- 7} c)^{2} = (4 a^{2} b^{- 7} c)^{2}

= (4 a^{2} b^{- 7} c)^{2}

指数の規則を適用する:

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

(4 a^{2} b^{- 7} c)^{2} = 4^{2} (a^{2})^{2} (b^{- 7})^{2} c^{2}

= 4^{2} (a^{2})^{2} (b^{- 7})^{2} c^{2}

4^{2} = 16

= 16 (a^{2})^{2} (b^{- 7})^{2} c^{2}

簡素化

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

= 16 a^{4} (b^{- 7})^{2} c^{2}

簡素化

(b^{- 7})^{2} : \frac{1}{b ^{14}}

= 16 a^{4} \frac{1}{b ^{14}} c^{2}

簡素化

16 a^{4} \frac{1}{b ^{14}} c^{2} : \frac{16 a ^{4} c ^{2}}{b ^{14}}

= \frac{16 a ^{4} c ^{2}}{b ^{14}}