vereinfachen 1/(sqrt(2)\sqrt[3]{2)}

Lösung

vereinfachen

\frac{1}{2 3 2}

\frac{1}{6 2 ^{5}}

Dezimale

0.56123 \dots

Schritte zur Lösung

\frac{1}{2 3 2}

Wende Radikal Regel an:

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

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

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

Wende Radikal Regel an:

n a = a^{\frac{1}{n}}

32 = 2^{\frac{1}{3}}

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

Wende Exponentenregel an:

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

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

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

\frac{1}{2} + \frac{1}{3} = \frac{5}{6}

= \frac{1}{2 ^{\frac{5}{6}}}

2^{\frac{5}{6}} = 6 2^{5}

= \frac{1}{6 2 ^{5}}

s im pl i f y \frac{- 6}{- 5}

\frac{7}{6} \div 3

s im pl i f y \frac{( \frac{x}{2} - 1 )}{( x - 2 )}

s im pl i f y - 9 + - 4 - 4 + i

e x p an d (4 s - 1) (2 s + 5)