vereinfachen 16^{(-2)/3}

Lösung

vereinfachen

1 6^{\frac{- 2}{3}}

\frac{1}{4 \cdot 2 ^{\frac{2}{3}}}

Dezimale

0.15749 \dots

Schritte zur Lösung

1 6^{\frac{- 2}{3}}

Primfaktorzerlegung von

16 : 2^{4}

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

Wende Exponentenregel an:

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

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

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

Wende Exponentenregel an:

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

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

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

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

= \frac{1}{4} \cdot 2^{\frac{- 2}{3}}

Wende Bruchregel an:

\frac{- a}{b} = - \frac{a}{b}

\frac{- 2}{3} = - \frac{2}{3}

= \frac{1}{4} \cdot 2^{- \frac{2}{3}}

Wende Exponentenregel an:

a^{- b} = \frac{1}{a ^{b}}

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

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

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

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

3 x + 3 = x + 7

f a c t or 2 x^{2} - 9 x + 4

x^{2} + 7 x - 3 = - 4 x - 21

s im pl i f y (- 2 + 3 i)^{2}

f a c t or 3 - 2 x - x^{2}