vereinfachen ((x^2y)^{-1/3}(xy)^{1/4})/((xy^{-2))^{1/12}}

Lösung

vereinfachen

\frac{( x ^{2} y ) ^{- \frac{1}{3}} ( x y ) ^{\frac{1}{4}}}{( x y ^{- 2} ) ^{\frac{1}{12}}}

\frac{y ^{\frac{1}{12}}}{x ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{( x ^{2} y ) ^{- \frac{1}{3}} ( x y ) ^{\frac{1}{4}}}{( x y ^{- 2} ) ^{\frac{1}{12}}}

Wende Exponentenregel an:

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

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

= \frac{( x ^{2} y ) ^{- \frac{1}{3}} x ^{\frac{1}{4}} y ^{\frac{1}{4}}}{( x y ^{- 2} ) ^{\frac{1}{12}}}

Vereinfache

(x y^{- 2})^{\frac{1}{12}} : x^{\frac{1}{12}} \frac{1}{y ^{\frac{1}{6}}}

= \frac{( x ^{2} y ) ^{- \frac{1}{3}} x ^{\frac{1}{4}} y ^{\frac{1}{4}}}{x ^{\frac{1}{12}} \frac{1}{y ^{\frac{1}{6}}}}

Vereinfache

\frac{x ^{\frac{1}{4}}}{x ^{\frac{1}{12}}} : x^{\frac{1}{6}}

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

Vereinfache

\frac{( x ^{2} y ) ^{- \frac{1}{3}} x ^{\frac{1}{6}} y ^{\frac{1}{4}}}{\frac{1}{y ^{\frac{1}{6}}}} : \frac{y ^{\frac{1}{12}}}{x ^{\frac{1}{2}}}

= \frac{y ^{\frac{1}{12}}}{x ^{\frac{1}{2}}}

f a c t or 2 x^{3} + 18 x^{2} + 66 x + 50

f a c t or 4 x^{3} - 12 y^{4}

x^{2} - 8 x + 12 \leq 0

f a c t or v^{2} - 8 v + 16

s im pl i f y 1280