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Beliebt Algebra >

vereinfachen \sqrt[3]{((-1)/(27))}^5

Lösung

vereinfachen

3 (\frac{- 1}{27})^{5}

Lösung

- \frac{3 ( - 1 ) ^{2}}{243}

+1

Dezimale

- 0.00411 \dots

Schritte zur Lösung

(3 \frac{- 1}{27})^{5}

Apply rule:

(a) = a

(\frac{- 1}{27}) = \frac{- 1}{27}

= (3 \frac{- 1}{27})^{5}

Wende Exponentenregel an:

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

(3 \frac{- 1}{27})^{3 + 2} = (3 \frac{- 1}{27})^{3} (3 \frac{- 1}{27})^{2}

= (3 \frac{- 1}{27})^{3} (3 \frac{- 1}{27})^{2}

Wende Exponentenregel an:

(n a)^{n} = a, n i s o dd or a \geq 0

(3 \frac{- 1}{27})^{3} = \frac{- 1}{27}

= \frac{- 1}{27} (3 \frac{- 1}{27})^{2}

Wende Radikal Regel an:

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

3 \frac{- 1}{27} = (\frac{- 1}{27})^{\frac{1}{3}}

= \frac{- 1}{27} ((\frac{- 1}{27})^{\frac{1}{3}})^{2}

Wende Exponentenregel an:

(a^{b})^{c} = a^{b c}, a \geq 0

((\frac{- 1}{27})^{\frac{1}{3}})^{2} = (\frac{- 1}{27})^{\frac{1}{3} \cdot 2}

= \frac{- 1}{27} (\frac{- 1}{27})^{\frac{1}{3} \cdot 2}

\frac{1}{3} \cdot 2 = \frac{2}{3}

= \frac{- 1}{27} (\frac{- 1}{27})^{\frac{2}{3}}

Wende Exponentenregel an:

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

\frac{- 1}{27} (\frac{- 1}{27})^{\frac{2}{3}} = (\frac{- 1}{27})^{1 + \frac{2}{3}}

= (\frac{- 1}{27})^{1 + \frac{2}{3}}

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

= (\frac{- 1}{27})^{\frac{5}{3}}

Wende Exponentenregel an:

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

= \frac{( - 1 ) ^{\frac{5}{3}}}{2 7 ^{\frac{5}{3}}}

2 7^{\frac{5}{3}} = 243

= \frac{( - 1 ) ^{\frac{5}{3}}}{243}

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

= \frac{- ( - 1 ) ^{\frac{2}{3}}}{243}

Wende Bruchregel an:

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

= - \frac{( - 1 ) ^{\frac{2}{3}}}{243}

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

= - \frac{3 ( - 1 ) ^{2}}{243}

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