vereinfachen \sqrt[6]{3^5}*\sqrt[6]{3^5}

Lösung

vereinfachen

6 3^{5} \cdot 6 3^{5}

3 3 3^{2}

Dezimale

6.24025 \dots

Schritte zur Lösung

6 3^{5} 6 3^{5}

Wende Radikal Regel an:

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

6 3^{5} = (3^{5})^{\frac{1}{6}}

= (3^{5})^{\frac{1}{6}} (3^{5})^{\frac{1}{6}}

Wende Exponentenregel an:

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

(3^{5})^{\frac{1}{6}} (3^{5})^{\frac{1}{6}} = (3^{5})^{\frac{1}{6} + \frac{1}{6}}

= (3^{5})^{\frac{1}{6} + \frac{1}{6}}

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

= (3^{5})^{\frac{1}{3}}

Wende Exponentenregel an:

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

= 3^{5 \cdot \frac{1}{3}}

5 \cdot \frac{1}{3} = \frac{5}{3}

= 3^{\frac{5}{3}}

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

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

Wende Exponentenregel an:

x^{a + b} = x^{a} x^{b}

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

Fasse zusammen

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

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

= 3 3 3^{2}

e x p an d x + 1 (x + 1)

\frac{400}{6}

s im pl i f y \frac{12}{30}

s im pl i f y \frac{1}{\frac{2}{2}}

s im pl i f y 1 - \frac{9}{x ^{2}}