vereinfachen (\sqrt[7]{x^2})/(\sqrt[5]{y^3)}

Lösung

vereinfachen

\frac{7 x ^{2}}{5 y ^{3}}

\frac{y ^{\frac{2}{5}} 7 x ^{2}}{y}

Schritte zur Lösung

\frac{7 x ^{2}}{5 y ^{3}}

Multipliziere mit dem Konjugat

\frac{( y ^{3} ) ^{\frac{4}{5}}}{( y ^{3} ) ^{\frac{4}{5}}}

= \frac{7 x ^{2} ( y ^{3} ) ^{\frac{4}{5}}}{5 y ^{3} ( y ^{3} ) ^{\frac{4}{5}}}

Vereinfache

7 x^{2} (y^{3})^{\frac{4}{5}} : y^{\frac{12}{5}} 7 x^{2}

5 y^{3} (y^{3})^{\frac{4}{5}} = y^{3}

= \frac{y ^{\frac{12}{5}} 7 x ^{2}}{y ^{3}}

y^{\frac{12}{5}} = y^{2 + \frac{2}{5}}, y^{3} = y^{2 + 1}

= \frac{y ^{\frac{2}{5} + 2} 7 x ^{2}}{y ^{2 + 1}}

Wende Exponentenregel an:

a^{b + c} = a^{b} a^{c}

y^{2 + \frac{2}{5}} = y^{2} y^{\frac{2}{5}}, y^{2 + 1} = y^{2} y^{1}

= \frac{y ^{2} y ^{\frac{2}{5}} 7 x ^{2}}{y ^{2} y ^{1}}

Streiche die gemeinsamen Faktoren:

y^{2}

= \frac{y ^{\frac{2}{5}} 7 x ^{2}}{y}

\frac{3}{5} t = - 12

s im pl i f y (6 v)^{2}

4 (- 3)^{3}

f a c t or (6 x^{3} - 2 x^{2} + x - 3) - (8 x^{2} - x - 3)

ln (3 - x) \leq 1 + ln (x)