vereinfachen (m^{5/4}n^{-4/5})^{7/3}

Lösung

vereinfachen

(m^{\frac{5}{4}} n^{- \frac{4}{5}})^{\frac{7}{3}}

\frac{m ^{\frac{35}{12}}}{n ^{\frac{28}{15}}}

Schritte zur Lösung

(m^{\frac{5}{4}} n^{- \frac{4}{5}})^{\frac{7}{3}}

Wende Exponentenregel an:

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

(m^{\frac{5}{4}} n^{- \frac{4}{5}})^{\frac{7}{3}} = (m^{\frac{5}{4}})^{\frac{7}{3}} (n^{- \frac{4}{5}})^{\frac{7}{3}}

= (m^{\frac{5}{4}})^{\frac{7}{3}} (n^{- \frac{4}{5}})^{\frac{7}{3}}

Vereinfache

(m^{\frac{5}{4}})^{\frac{7}{3}} : m^{\frac{35}{12}}

= m^{\frac{35}{12}} (n^{- \frac{4}{5}})^{\frac{7}{3}}

Vereinfache

(n^{- \frac{4}{5}})^{\frac{7}{3}} : \frac{1}{n ^{\frac{28}{15}}}

= m^{\frac{35}{12}} \frac{1}{n ^{\frac{28}{15}}}

Vereinfache

m^{\frac{35}{12}} \frac{1}{n ^{\frac{28}{15}}} : \frac{m ^{\frac{35}{12}}}{n ^{\frac{28}{15}}}

= \frac{m ^{\frac{35}{12}}}{n ^{\frac{28}{15}}}

(2 x + 1)^{2} = 4 + (x + 2) (x - 2)

(x - 7) (- 4 x - 2) = 0

2 x + 5 < 3 x + 4

x (x + 4) > 0

- 4 + 2 x = 4 x + 8