vereinfachen \sqrt[3]{2x^8}*\sqrt[3]{16x^9}

Lösung

vereinfachen

3 2 x^{8} \cdot 3 16 x^{9}

2 3 2^{2} x^{5} 3 x^{2}

Schritte zur Lösung

3 2 x^{8} 3 16 x^{9}

Vereinfache

3 2 x^{8} : 32 x^{2} 3 x^{2}

= 32 x^{2} 3 x^{2} 3 16 x^{9}

Vereinfache

3 16 x^{9} : 232 x^{3}

= 32 x^{2} 3 x^{2} \cdot 232 x^{3}

Wende Radikal Regel an:

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

32 = 2^{\frac{1}{3}}

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

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

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

Vereinfache

x^{2} x^{3} : x^{5}

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

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

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

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

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

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

= 2 3 2^{2} x^{5} 3 x^{2}

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