vereinfachen 243^{7/10}*243^{1/10}

Lösung

vereinfachen

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}}

81

Schritte zur Lösung

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}}

Wende Exponentenregel an:

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

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}} = 24 3^{\frac{7}{10} + \frac{1}{10}}

= 24 3^{\frac{7}{10} + \frac{1}{10}}

\frac{7}{10} + \frac{1}{10} = \frac{4}{5}

= 24 3^{\frac{4}{5}}

Faktorisiere die Zahl:

243 = 3^{5}

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

Wende Exponentenregel an:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{5 \cdot \frac{4}{5}}

5 \cdot \frac{4}{5} = 4

= 3^{4}

3^{4} = 81

= 81

f a c t or x^{3} - 729

\frac{4}{5} (x - 2) < \frac{1}{3} (x - 6)

3 x^{2} - 2.4 x + 0.41 = 0

s im pl i f y 3 0^{4}

(x - 4)^{\frac{2}{3}} < (2 x)^{\frac{1}{3}}