vereinfachen (\sqrt[6]{x^8y^{10}})/(\sqrt[3]{xy^2)}

Lösung

vereinfachen

\frac{6 x ^{8} y ^{10}}{3 x y ^{2}}

x y

Schritte zur Lösung

\frac{6 x ^{8} y ^{10}}{3 x y ^{2}}

Wende Radikal Regel an:

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

6 x^{8} y^{10} = (x^{8} y^{10})^{\frac{1}{6}}

= \frac{( x ^{8} y ^{10} ) ^{\frac{1}{6}}}{3 x y ^{2}}

Wende Radikal Regel an:

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

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

= \frac{( x ^{8} y ^{10} ) ^{\frac{1}{6}}}{( x y ^{2} ) ^{\frac{1}{3}}}

Vereinfache

(x^{8} y^{10})^{\frac{1}{6}} : x^{\frac{4}{3}} y^{\frac{5}{3}}

= \frac{x ^{\frac{4}{3}} y ^{\frac{5}{3}}}{( x y ^{2} ) ^{\frac{1}{3}}}

Vereinfache

(x y^{2})^{\frac{1}{3}} : x^{\frac{1}{3}} y^{\frac{2}{3}}

= \frac{x ^{\frac{4}{3}} y ^{\frac{5}{3}}}{x ^{\frac{1}{3}} y ^{\frac{2}{3}}}

Vereinfache

\frac{x ^{\frac{4}{3}}}{x ^{\frac{1}{3}}} : x

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

Vereinfache

\frac{y ^{\frac{5}{3}}}{y ^{\frac{2}{3}}} : y

= x y

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