簡約 (ln(c^{-4}))(ln(a/(b^2)))^{-4}

解

簡約

(ln (c^{- 4})) (ln (\frac{a}{b ^{2}}))^{- 4}

- \frac{4 ln ( c )}{( ln ( a ) - 2 ln ( b ) ) ^{4}}

解答ステップ

(ln (c^{- 4})) (ln (\frac{a}{b ^{2}}))^{- 4}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( ln ( \frac{a}{b ^{2}} ) ) ^{4}} ln (c^{- 4})

簡素化

ln (c^{- 4}) : - 4 ln (c)

= - 4 \cdot \frac{1}{ln ^{4} ( \frac{a}{b ^{2}} )} ln (c)

分数を乗じる:

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

= - \frac{1 \cdot 4 ln ( c )}{ln ^{4} ( \frac{a}{b ^{2}} )}

数を乗じる:

1 \cdot 4 = 4

= - \frac{4 ln ( c )}{ln ^{4} ( \frac{a}{b ^{2}} )}

ln^{4} (\frac{a}{b ^{2}}) = (ln (a) - 2 ln (b))^{4}

= - \frac{4 ln ( c )}{( ln ( a ) - 2 ln ( b ) ) ^{4}}