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Beliebt Algebra >

vereinfachen (2/3)^5(2/3)^{-3}(2/3)^4(2/3)^5

Lösung

vereinfachen

(\frac{2}{3})^{5} (\frac{2}{3})^{- 3} (\frac{2}{3})^{4} (\frac{2}{3})^{5}

Lösung

\frac{2048}{177147}

+1

Dezimale

0.01156 \dots

Schritte zur Lösung

(\frac{2}{3})^{5} (\frac{2}{3})^{- 3} (\frac{2}{3})^{4} (\frac{2}{3})^{5}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

(\frac{2}{3})^{5} (\frac{2}{3})^{- 3} (\frac{2}{3})^{4} (\frac{2}{3})^{5} = (\frac{2}{3})^{5 - 3 + 4 + 5}

= (\frac{2}{3})^{5 - 3 + 4 + 5}

Addiere/Subtrahiere die Zahlen:

5 - 3 + 4 + 5 = 11

= (\frac{2}{3})^{11}

Wende Exponentenregel an:

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

= \frac{2 ^{11}}{3 ^{11}}

2^{11} = 2048

= \frac{2048}{3 ^{11}}

3^{11} = 177147

= \frac{2048}{177147}

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