vereinfachen 144^{1/4}

Lösung

vereinfachen

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

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

Dezimale

3.46410 \dots

Schritte zur Lösung

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

Faktorisiere die Zahl:

144 = 1 2^{2}

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

Wende Exponentenregel an:

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

= 1 2^{2 \cdot \frac{1}{4}}

2 \cdot \frac{1}{4} = \frac{1}{2}

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

Primfaktorzerlegung von

12 : 2^{2} \cdot 3

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

Wende Exponentenregel an:

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

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

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

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

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

∣ x - 12 ∣ \leq ∣ 4 - x ∣

f a c t or 27 x^{3} + 72 y^{3}

2 x^{2} + x + 6 = 0

3 a \geq 12

f a c t or (x + 2)^{2} - 2