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Beliebt Algebra >

vereinfachen (sqrt(3/5))^5

Lösung

vereinfachen

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

Lösung

\frac{9 3}{25 5}

+1

Dezimale

0.27885 \dots

Schritte zur Lösung

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

Wende Exponentenregel an:

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

(\frac{3}{5})^{4 + 1} = (\frac{3}{5})^{4} \frac{3}{5}

= (\frac{3}{5})^{4} \frac{3}{5}

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

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

Wende Exponentenregel an:

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

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

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

Wende Radikal Regel an:

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

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

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

Wende Exponentenregel an:

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

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

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

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

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

Wende Exponentenregel an:

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

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

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

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

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

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

3^{2} = 9

= \frac{9 3}{5 ^{2} 5}

5^{2} = 25

= \frac{9 3}{25 5}

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