vereinfachen (2/3)^4(9/4)^4(4/3)^4

Lösung

vereinfachen

(\frac{2}{3})^{4} (\frac{9}{4})^{4} (\frac{4}{3})^{4}

16

Schritte zur Lösung

(\frac{2}{3})^{4} (\frac{9}{4})^{4} (\frac{4}{3})^{4}

(\frac{2}{3})^{4} (\frac{9}{4})^{4} = \frac{1}{\frac{16}{81}}

= \frac{1}{\frac{16}{81}} (\frac{4}{3})^{4}

Wende Bruchregel an:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= (\frac{4}{3})^{4} \frac{81}{16}

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

= \frac{81}{16} \cdot \frac{4 ^{4}}{3 ^{4}}

Multipliziere Brüche:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{81 \cdot 4 ^{4}}{16 \cdot 3 ^{4}}

Faktorisiere

81 : 3^{4}

Faktorisiere

4^{4} : 2^{8}

Faktorisiere

16 : 2^{4}

= \frac{2 ^{8} \cdot 3 ^{4}}{2 ^{4} \cdot 3 ^{4}}

Streiche

\frac{3 ^{4} \cdot 2 ^{8}}{2 ^{4} \cdot 3 ^{4}} : 2^{4}

= 2^{4}

2^{4} = 16

= 16

2 (x - 2) = - (4 - x)

x^{2} - 8 x + 14 = 0

5 x^{2} - 2 x - 24 = 0

f a c t or x^{2} - 9 x + 4 x - 36

- 18 < 9 x