vereinfachen (9^{2/3})(3)(3^{2/3})

Lösung

vereinfachen

(9^{\frac{2}{3}}) (3) (3^{\frac{2}{3}})

27

Schritte zur Lösung

(9^{\frac{2}{3}}) (3) (3^{\frac{2}{3}})

(9^{\frac{2}{3}}) (3) (3^{\frac{2}{3}}) = 9^{\frac{2}{3}} \cdot 3 \cdot 3^{\frac{2}{3}}

= 9^{\frac{2}{3}} \cdot 3 \cdot 3^{\frac{2}{3}}

3 \cdot 3^{\frac{2}{3}} = 3^{\frac{5}{3}}

= 9^{\frac{2}{3}} \cdot 3^{\frac{5}{3}}

Faktorisiere die ganze Zahl

9 = 3^{2}

= (3^{2})^{\frac{2}{3}} \cdot 3^{\frac{5}{3}}

Wende Exponentenregel an:

(a^{b})^{c} = a^{b c}

(3^{2})^{\frac{2}{3}} = 3^{2 \cdot \frac{2}{3}}

= 3^{2 \cdot \frac{2}{3}} \cdot 3^{\frac{5}{3}}

Fasse zusammen

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

Wende Exponentenregel an:

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

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

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

Füge

\frac{4}{3} + \frac{5}{3}

zusammen:

3

= 3^{3}

3^{3} = 27

= 27

6 - 3 x = - 3

f a c t or 64 x^{2} - 25

- 8 c + 3 = c + 8 - 10 c

f a c t or 16 x^{3} - 12 x^{2} + 20 x - 15

4 x^{2} + 10 = 11