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

Lösung

vereinfachen

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

\frac{42875}{216}

Dezimale

198.49537 \dots

Schritte zur Lösung

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

(\frac{2}{5})^{- 3} = \frac{125}{8}

= \frac{125}{8} (\frac{3}{7})^{- 3}

Wende Exponentenregel an:

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

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

= \frac{125}{8} \cdot \frac{1}{( \frac{3}{7} ) ^{3}}

(\frac{3}{7})^{3} = \frac{27}{343}

= \frac{125}{8} \cdot \frac{1}{\frac{27}{343}}

Wende Bruchregel an:

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

= \frac{125}{8} \cdot \frac{343}{27}

\frac{125}{8} \cdot \frac{343}{27} = \frac{42875}{216}

= \frac{42875}{216}

s im pl i f y (\frac{2}{3})^{5} \cdot (\frac{2}{3})^{3}

e x p an d (x - 1) (x + 1)

s im pl i f y \frac{4}{2}

e x p an d (x + 4) (x - 4)

s im pl i f y \frac{3}{6}