vereinfachen (27x^{-1})^{(-2)/3}

Lösung

vereinfachen

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

\frac{x ^{\frac{2}{3}}}{9}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

(27 x^{- 1})^{\frac{- 2}{3}} = 2 7^{\frac{- 2}{3}} (x^{- 1})^{\frac{- 2}{3}}

= 2 7^{\frac{- 2}{3}} (x^{- 1})^{\frac{- 2}{3}}

2 7^{\frac{- 2}{3}} = \frac{1}{9}

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

Wende Exponentenregel an:

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

angenommen

a \geq 0

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

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

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

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

Vereinfache

\frac{1}{9} x^{\frac{2}{3}} : \frac{x ^{\frac{2}{3}}}{9}

= \frac{x ^{\frac{2}{3}}}{9}

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