vereinfachen (27\sqrt[3]{z^2})^{1/3}

Lösung

vereinfachen

(27 3 z^{2})^{\frac{1}{3}}

3 z^{\frac{2}{9}}

Schritte zur Lösung

(27 3 z^{2})^{\frac{1}{3}}

Wende Exponentenregel an:

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

(27 3 z^{2})^{\frac{1}{3}} = 2 7^{\frac{1}{3}} (3 z^{2})^{\frac{1}{3}}

= 2 7^{\frac{1}{3}} (3 z^{2})^{\frac{1}{3}}

2 7^{\frac{1}{3}} = 3

= 3 (3 z^{2})^{\frac{1}{3}}

Wende Radikal Regel an:

n a^{m} = a^{\frac{m}{n}},

angenommen

a \geq 0

3 z^{2} = z^{\frac{2}{3}}

= 3 (z^{\frac{2}{3}})^{\frac{1}{3}}

Wende Exponentenregel an:

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

angenommen

a \geq 0

(z^{\frac{2}{3}})^{\frac{1}{3}} = z^{\frac{2}{3} \cdot \frac{1}{3}}

= 3 z^{\frac{2}{3} \cdot \frac{1}{3}}

\frac{2}{3} \cdot \frac{1}{3} = \frac{2}{9}

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

s im pl i f y \frac{120}{72} \cdot 9

- x^{2} + 14 x = 48

s im pl i f y (a^{\frac{1}{2}} \cdot b^{\frac{1}{3}})^{\frac{1}{2}}

2 x - 7 = - 3 x + 18

f a c t or x^{3} - 8 y^{3}