vereinfachen (1/3 x^{-2/3})^2

Lösung

vereinfachen

(\frac{1}{3} x^{- \frac{2}{3}})^{2}

\frac{1}{9 x ^{\frac{4}{3}}}

Schritte zur Lösung

(\frac{1}{3} x^{- \frac{2}{3}})^{2}

Wende Exponentenregel an:

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

(\frac{1}{3} x^{- \frac{2}{3}})^{2} = (\frac{1}{3})^{2} (x^{- \frac{2}{3}})^{2}

= (\frac{1}{3})^{2} (x^{- \frac{2}{3}})^{2}

(\frac{1}{3})^{2} = \frac{1}{9}

= \frac{1}{9} (x^{- \frac{2}{3}})^{2}

Wende Exponentenregel an:

(a^{b})^{c} = a^{b c},

angenommen

a \geq 0

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

= \frac{1}{9} x^{- \frac{2}{3} \cdot 2}

- \frac{2}{3} \cdot 2 = - \frac{4}{3}

= \frac{1}{9} x^{- \frac{4}{3}}

Wende Exponentenregel an:

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

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

= \frac{1}{9} \cdot \frac{1}{x ^{\frac{4}{3}}}

Vereinfache

\frac{1}{9} \cdot \frac{1}{x ^{\frac{4}{3}}} : \frac{1}{9 x ^{\frac{4}{3}}}

= \frac{1}{9 x ^{\frac{4}{3}}}

6 x^{2} - 6 x - 1 = 0

s im pl i f y \frac{1 + i}{i} - \frac{3}{4 - i}

s im pl i f y \frac{7}{4 - 9 i}

z^{2} - 6 z + 9 = - 4

f a c t or - 4 x^{2} + 36