簡約 [(-x^2)^9]^3[(-x)^{-6}]^5

解

簡約

[(- x^{2})^{9}]^{3} [(- x)^{- 6}]^{5}

- x^{24}

解答ステップ

[(- x^{2})^{9}]^{3} [(- x)^{- 6}]^{5}

[(- x^{2})^{9}]^{3} : (- x^{2})^{27}

= (- x^{2})^{27} [(- x)^{- 6}]^{5}

[(- x)^{- 6}]^{5} : (- x)^{- 30}

= (- x^{2})^{27} (- x)^{- 30}

(- x^{2})^{27} = - x^{54}

= - x^{54} (- x)^{- 30}

(- x)^{- 30} = \frac{1}{x ^{30}}

= - \frac{1}{x ^{30}} x^{54}

分数を乗じる:

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

= - \frac{1 \cdot x ^{54}}{x ^{30}}

乗算:

1 \cdot x^{54} = x^{54}

= - \frac{x ^{54}}{x ^{30}}

指数の規則を適用する:

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

\frac{x ^{54}}{x ^{30}} = x^{54 - 30}

= x^{54 - 30}

数を引く:

54 - 30 = 24

= - x^{24}