vereinfachen (7/2)^3(11/7)^2(2/11)^{-5}

Lösung

vereinfachen

(\frac{7}{2})^{3} \cdot (\frac{11}{7})^{2} \cdot (\frac{2}{11})^{- 5}

\frac{136410197}{256}

Dezimale

532852.33203 \dots

Schritte zur Lösung

(\frac{7}{2})^{3} (\frac{11}{7})^{2} (\frac{2}{11})^{- 5}

(\frac{7}{2})^{3} = \frac{343}{8}

= \frac{343}{8} (\frac{11}{7})^{2} (\frac{2}{11})^{- 5}

(\frac{11}{7})^{2} = \frac{121}{49}

= \frac{343}{8} \cdot \frac{121}{49} (\frac{2}{11})^{- 5}

Wende Exponentenregel an:

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

(\frac{2}{11})^{- 5} = \frac{1}{( \frac{2}{11} ) ^{5}}

= \frac{343}{8} \cdot \frac{121}{49} \cdot \frac{1}{( \frac{2}{11} ) ^{5}}

(\frac{2}{11})^{5} = \frac{32}{161051}

= \frac{343}{8} \cdot \frac{121}{49} \cdot \frac{1}{\frac{32}{161051}}

Wende Bruchregel an:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{343}{8} \cdot \frac{121}{49} \cdot \frac{161051}{32}

\frac{343}{8} \cdot \frac{121}{49} \cdot \frac{161051}{32} = \frac{136410197}{256}

= \frac{136410197}{256}

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