vereinfachen t^{-1/3}x^{-4/3}(5t^3x^2-8tx^3)

Lösung

vereinfachen

t^{- \frac{1}{3}} x^{- \frac{4}{3}} (5 t^{3} x^{2} - 8 t x^{3})

t^{\frac{2}{3}} x^{\frac{2}{3}} (5 t^{2} - 8 x)

Schritte zur Lösung

t^{- \frac{1}{3}} x^{- \frac{4}{3}} (5 t^{3} x^{2} - 8 t x^{3})

Wende Exponentenregel an:

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

t^{- \frac{1}{3}} = \frac{1}{t ^{\frac{1}{3}}}

= \frac{1}{t ^{\frac{1}{3}}} x^{- \frac{4}{3}} (5 t^{3} x^{2} - 8 t x^{3})

Wende Exponentenregel an:

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

x^{- \frac{4}{3}} = \frac{1}{x ^{\frac{4}{3}}}

= \frac{1}{t ^{\frac{1}{3}}} \cdot \frac{1}{x ^{\frac{4}{3}}} (5 t^{3} x^{2} - 8 t x^{3})

Wende Bruchregel an:

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

= \frac{1 \cdot 1 \cdot ( 5 t ^{3} x ^{2} - 8 t x ^{3} )}{t ^{\frac{1}{3}} x ^{\frac{4}{3}}}

Vereinfache

1 \cdot 1 \cdot (5 t^{3} x^{2} - 8 t x^{3}) : 5 t^{3} x^{2} - 8 t x^{3}

= \frac{5 t ^{3} x ^{2} - 8 t x ^{3}}{t ^{\frac{1}{3}} x ^{\frac{4}{3}}}

Faktorisiere

5 t^{3} x^{2} - 8 t x^{3} : t x^{2} (5 t^{2} - 8 x)

= \frac{t x ^{2} ( 5 t ^{2} - 8 x )}{t ^{\frac{1}{3}} x ^{\frac{4}{3}}}

Vereinfache

\frac{t}{t ^{\frac{1}{3}}} : t^{\frac{2}{3}}

= \frac{t ^{\frac{2}{3}} x ^{2} ( 5 t ^{2} - 8 x )}{x ^{\frac{4}{3}}}

Vereinfache

\frac{x ^{2}}{x ^{\frac{4}{3}}} : x^{\frac{2}{3}}

= t^{\frac{2}{3}} x^{\frac{2}{3}} (5 t^{2} - 8 x)

e x p an d \frac{( 3 x - 4 ) ( 3 - 2 x )}{4 x ^{2} - 1}

s im pl i f y \frac{13}{3}

s im pl i f y 66 \cdot 3 6^{2}

s im pl i f y (e^{- a x^{2}})^{2}

s im pl i f y 4^{2 a}