vereinfachen 256^{4/3}

Lösung

vereinfachen

25 6^{\frac{4}{3}}

1024 \cdot 2^{\frac{2}{3}}

Dezimale

1625.49867 \dots

Schritte zur Lösung

25 6^{\frac{4}{3}}

Primfaktorzerlegung von

256 : 2^{8}

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

Wende Exponentenregel an:

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

2^{8} = 2^{6} \cdot 2^{2}

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

Wende Exponentenregel an:

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

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

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

(2^{6})^{\frac{4}{3}} = 256

= 256 (2^{2})^{\frac{4}{3}}

Wende Exponentenregel an:

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

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

= 256 \cdot 2^{2 \cdot \frac{4}{3}}

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

= 256 \cdot 2^{\frac{8}{3}}

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

= 256 \cdot 4 \cdot 2^{\frac{2}{3}}

Multipliziere die Zahlen:

256 \cdot 4 = 1024

= 1024 \cdot 2^{\frac{2}{3}}

- 8 + 4 \div 2 + 5

f a c t or x y - 2 x + 4 y - 8

3 x^{2} + 48 = 0

- 4 x = 7

f a c t or 64 - k^{2}