vereinfachen (((2/3)^2)^3)^{-3}

Lösung

vereinfachen

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

\frac{387420489}{262144}

Dezimale

1477.89188 \dots

Schritte zur Lösung

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

((\frac{2}{3})^{2})^{3} : (\frac{2}{3})^{6}

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

Wende Exponentenregel an:

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

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

((\frac{2}{3})^{6})^{3} : (\frac{2}{3})^{18}

= \frac{1}{( \frac{2}{3} ) ^{18}}

Wende Exponentenregel an:

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

(\frac{2}{3})^{18} = \frac{2 ^{18}}{3 ^{18}}

= \frac{1}{\frac{2 ^{18}}{3 ^{18}}}

Wende Bruchregel an:

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

= \frac{3 ^{18}}{2 ^{18}}

3^{18} = 387420489

= \frac{387420489}{2 ^{18}}

2^{18} = 262144

= \frac{387420489}{262144}

s im pl i f y - 7 e^{- 3} x

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