vereinfachen ((6^{1/5})/(6^{2/5)})^3

Lösung

vereinfachen

(\frac{6 ^{\frac{1}{5}}}{6 ^{\frac{2}{5}}})^{3}

\frac{1}{6 ^{\frac{3}{5}}}

Dezimale

0.34127 \dots

Schritte zur Lösung

(\frac{6 ^{\frac{1}{5}}}{6 ^{\frac{2}{5}}})^{3}

Wende Exponentenregel an:

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

= \frac{( 6 ^{\frac{1}{5}} ) ^{3}}{( 6 ^{\frac{2}{5}} ) ^{3}}

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

= \frac{6 ^{\frac{3}{5}}}{( 6 ^{\frac{2}{5}} ) ^{3}}

(6^{\frac{2}{5}})^{3} = 6 \cdot 6^{\frac{1}{5}}

= \frac{6 ^{\frac{3}{5}}}{6 \cdot 6 ^{\frac{1}{5}}}

Wende Exponentenregel an:

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

\frac{6 ^{\frac{3}{5}}}{6} = \frac{1}{6 ^{1 - \frac{3}{5}}}

= \frac{1}{6 ^{\frac{1}{5}} \cdot 6 ^{- \frac{3}{5} + 1}}

Subtrahiere die Zahlen:

1 - \frac{3}{5} = \frac{2}{5}

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

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

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

Ziehe Brüche zusammen

\frac{2}{5} + \frac{1}{5} : \frac{3}{5}

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

x^{2} - 9 x + 14 = 0

- 7 d = 15

3 x^{2} - 6 = 23 x + 2

3 (x + 7) < 7 (x + 2)

s im pl i f y (\frac{14 x}{15 y}) (\frac{25 y}{24})