vereinfachen (b^{2/3}c^{2/5})(b^{4/9}c^{9/10})

Lösung

vereinfachen

(b^{\frac{2}{3}} \cdot c^{\frac{2}{5}}) (b^{\frac{4}{9}} \cdot c^{\frac{9}{10}})

b^{\frac{10}{9}} c^{\frac{13}{10}}

Schritte zur Lösung

(b^{\frac{2}{3}} c^{\frac{2}{5}}) (b^{\frac{4}{9}} c^{\frac{9}{10}})

Wende Exponentenregel an:

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

b^{\frac{2}{3}} b^{\frac{4}{9}} = b^{\frac{2}{3} + \frac{4}{9}}

= c^{\frac{2}{5}} b^{\frac{2}{3} + \frac{4}{9}} c^{\frac{9}{10}}

Wende Exponentenregel an:

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

c^{\frac{2}{5}} c^{\frac{9}{10}} = c^{\frac{2}{5} + \frac{9}{10}}

= b^{\frac{2}{3} + \frac{4}{9}} c^{\frac{2}{5} + \frac{9}{10}}

b^{\frac{2}{3} + \frac{4}{9}} = b^{\frac{10}{9}}

= b^{\frac{10}{9}} c^{\frac{2}{5} + \frac{9}{10}}

c^{\frac{2}{5} + \frac{9}{10}} = c^{\frac{13}{10}}

= b^{\frac{10}{9}} c^{\frac{13}{10}}

s im pl i f y (6 y^{\frac{1}{2}}) (9 y^{\frac{1}{2}})

s im pl i f y (3 x^{2} y^{4}) (5 a^{2} x^{3} y^{8})

s im pl i f y 1 + u^{2} v \cdot u^{4} v^{2} + 1

s im pl i f y \frac{x ^{2} - 7 x + 10}{x - 5}

s im pl i f y (2 x^{2}) (4 x^{3})