vereinfachen sqrt(\sqrt[4]{\sqrt[3]{\sqrt[5]{23)}}}

Lösung

vereinfachen

43523

12023

Dezimale

1.02647 \dots

Schritte zur Lösung

43523

3523 : 1523

= 41523

Wende Radikal Regel an:

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

= ((1523)^{\frac{1}{4}})^{\frac{1}{2}}

Wende Exponentenregel an:

(a^{b})^{c} = a^{b c}

= (1523)^{\frac{1}{4} \cdot \frac{1}{2}}

\frac{1}{4} \cdot \frac{1}{2} = \frac{1}{8}

= (1523)^{\frac{1}{8}}

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

= 81523

Wende Radikal Regel an:

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

= (2 3^{\frac{1}{15}})^{\frac{1}{8}}

Wende Exponentenregel an:

(a^{b})^{c} = a^{b c}

= 2 3^{\frac{1}{15} \cdot \frac{1}{8}}

\frac{1}{15} \cdot \frac{1}{8} = \frac{1}{120}

= 2 3^{\frac{1}{120}}

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

= 12023

s im pl i f y 43 \cdot 5 3^{2}

s im pl i f y 1 e^{- s t}

j o in 18325 x^{2} 3 x^{2}

f (x) = sin^{2} (x) \cdot cos^{2} (x)

s im pl i f y 2^{16} \cdot 4^{- 8} \cdot 8^{4} \cdot 1 6^{- 2}