vereinfachen (\sqrt[3]{x^2-3x^{-3}})^{sqrt((2x-x^2))}

Lösung

vereinfachen

(3 x^{2} - 3 x^{- 3})^{(2 x - x^{2})}

\frac{( x ^{5} - 3 ) ^{\frac{2 x - x ^{2}}{3}}}{x ^{2 x - x^{2}}}

Schritte zur Lösung

(3 x^{2} - 3 x^{- 3})^{2 x - x^{2}}

Apply rule:

(a) = a

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

= (3 x^{2} - 3 x^{- 3})^{2 x - x^{2}}

Vereinfache

3 x^{2} - 3 x^{- 3} : \frac{3 x ^{5} - 3}{x}

= (\frac{3 x ^{5} - 3}{x})^{2 x - x^{2}}

Wende Exponentenregel an:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 x ^{5} - 3 ) ^{2 x - x^{2}}}{x ^{2 x - x^{2}}}

(3 x^{5} - 3)^{2 x - x^{2}} = (x^{5} - 3)^{\frac{2 x - x ^{2}}{3}}

= \frac{( x ^{5} - 3 ) ^{\frac{2 x - x ^{2}}{3}}}{x ^{2 x - x^{2}}}

s im pl i f y 5 (5 x^{2})

s im pl i f y (3 \frac{4}{6})^{6}

s im pl i f y (e^{- x}) (e^{- x} - x e^{- x})

s im pl i f y 2 (x - 1)^{2} (x + 1)^{2} (x - 3)

s im pl i f y \frac{e ^{x^{2}}}{e ^{x^{2}}}