vereinfachen 144^{1/3}

Lösung

vereinfachen

14 4^{\frac{1}{3}}

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

Dezimale

5.24148 \dots

Schritte zur Lösung

14 4^{\frac{1}{3}}

Primfaktorzerlegung von

144 : 2^{4} \cdot 3^{2}

= (2^{4} \cdot 3^{2})^{\frac{1}{3}}

Wende Exponentenregel an:

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

2^{4} \cdot 3^{2} = 2^{3} \cdot 2 \cdot 3^{2}

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

Wende Exponentenregel an:

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

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

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

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

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

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

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

9 + \frac{a}{6} = 8

\frac{- 5 u + 4}{2} = \frac{u}{4}

2 k^{2} + 9 k = - 7

\frac{1}{4} - \frac{1}{3} x = \frac{1}{3}

(2 x - 1)^{2} = 9