vereinfachen \sqrt[5]{(2/3)^{-2}}

Lösung

vereinfachen

5 (\frac{2}{3})^{- 2}

5 \frac{9}{4}

Dezimale

1.17607 \dots

Schritte zur Lösung

5 (\frac{2}{3})^{- 2}

Wende Radikal Regel an:

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

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

Wende Exponentenregel an:

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

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

(- 2) \frac{1}{5} = - \frac{2}{5}

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

Wende Exponentenregel an:

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

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

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

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

Wende Bruchregel an:

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

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

Fasse gleiche Potenzen zusammen:

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = m \frac{x ^{a}}{y ^{b}}

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

\frac{3 ^{2}}{2 ^{2}} = \frac{9}{4}

= 5 \frac{9}{4}

s im pl i f y 1.62 \cdot 1 0^{- 13}

s im pl i f y (3.2 x 1 0^{- 19}) (9.6 x 1 0^{5})

s im pl i f y (x - 2)^{2} (x - 3)^{2} (x + 5)

s im pl i f y 1021 (1 0^{- 4}) e^{- 0.001 (200)}

s im pl i f y e^{- 5 x} \cdot \frac{2}{5} e^{5 x}