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Beliebt Algebra >

vereinfachen {[((2^3)/(5^3))^{-3}]^2}^{-1/9}

Lösung

vereinfachen

⎩ ⎨ ⎧ [(\frac{2 ^{3}}{5 ^{3}})^{- 3}]^{2} ⎭ ⎬ ⎫^{- \frac{1}{9}}

Lösung

\frac{4}{25}

+1

Dezimale

0.16

Schritte zur Lösung

⎩ ⎨ ⎧ [(\frac{2 ^{3}}{5 ^{3}})^{- 3}]^{2} ⎭ ⎬ ⎫^{- \frac{1}{9}}

[(\frac{2 ^{3}}{5 ^{3}})^{- 3}]^{2} : (\frac{2 ^{3}}{5 ^{3}})^{- 6}

= {(\frac{2 ^{3}}{5 ^{3}})^{- 6}}^{- \frac{1}{9}}

Wende Exponentenregel an:

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

= \frac{1}{( ( \frac{2 ^{3}}{5 ^{3}} ) ^{- 6} ) ^{\frac{1}{9}}}

((\frac{2 ^{3}}{5 ^{3}})^{- 6})^{\frac{1}{9}} : (\frac{2 ^{3}}{5 ^{3}})^{- \frac{2}{3}}

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

Wende Exponentenregel an:

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

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

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

Wende Exponentenregel an:

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

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

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

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

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

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

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

Wende Bruchregel an:

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

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

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

Wende Bruchregel an:

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

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

2^{2} = 4

= \frac{4}{5 ^{2}}

5^{2} = 25

= \frac{4}{25}

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