vereinfachen (16x^{3/2})^{1/4}

Lösung

vereinfachen

(16 x^{\frac{3}{2}})^{\frac{1}{4}}

2 x^{\frac{3}{8}}

Schritte zur Lösung

(16 x^{\frac{3}{2}})^{\frac{1}{4}}

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

(16 x^{\frac{3}{2}})^{\frac{1}{4}} = 1 6^{\frac{1}{4}} (x^{\frac{3}{2}})^{\frac{1}{4}}

= 1 6^{\frac{1}{4}} (x^{\frac{3}{2}})^{\frac{1}{4}}

1 6^{\frac{1}{4}} = 2

= 2 (x^{\frac{3}{2}})^{\frac{1}{4}}

Wende Exponentenregel an:

(a^{b})^{c} = a^{b c},

angenommen

a \geq 0

(x^{\frac{3}{2}})^{\frac{1}{4}} = x^{\frac{3}{2} \cdot \frac{1}{4}}

= 2 x^{\frac{3}{2} \cdot \frac{1}{4}}

\frac{3}{2} \cdot \frac{1}{4} = \frac{3}{8}

= 2 x^{\frac{3}{8}}

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