vereinfachen 64^{3/4}

Lösung

vereinfachen

6 4^{\frac{3}{4}}

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

Dezimale

22.62741 \dots

Schritte zur Lösung

6 4^{\frac{3}{4}}

Primfaktorzerlegung von

64 : 2^{6}

= (2^{6})^{\frac{3}{4}}

Wende Exponentenregel an:

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

2^{6} = 2^{4} \cdot 2^{2}

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

Wende Exponentenregel an:

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

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

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

(2^{4})^{\frac{3}{4}} = 8

= 8 (2^{2})^{\frac{3}{4}}

Wende Exponentenregel an:

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

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

= 8 \cdot 2^{2 \cdot \frac{3}{4}}

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

= 8 \cdot 2^{\frac{3}{2}}

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

= 8 \cdot 2 \cdot 2^{\frac{1}{2}}

Multipliziere die Zahlen:

8 \cdot 2 = 16

= 16 \cdot 2^{\frac{1}{2}}

f a c t or x^{4} + 11 x^{2} + 24

4 x^{2} + 7 x - 2 = 0

f a c t or 12 x^{2} + 17 x + 6

2 (12 - 8 x) = x - 11 x

s im pl i f y - i^{2}