vereinfachen ((8x^{-1/2}y^2)/(4x^{2/3)y^{-1/4}})^3

Lösung

vereinfachen

(\frac{8 x ^{- \frac{1}{2}} y ^{2}}{4 x ^{\frac{2}{3}} y ^{- \frac{1}{4}}})^{3}

\frac{8 y ^{\frac{27}{4}}}{x ^{\frac{7}{2}}}

Schritte zur Lösung

(\frac{8 x ^{- \frac{1}{2}} y ^{2}}{4 x ^{\frac{2}{3}} y ^{- \frac{1}{4}}})^{3}

Wende Exponentenregel an:

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

= \frac{( 8 x ^{- \frac{1}{2}} y ^{2} ) ^{3}}{( 4 x ^{\frac{2}{3}} y ^{- \frac{1}{4}} ) ^{3}}

Vereinfache

(8 x^{- \frac{1}{2}} y^{2})^{3} : \frac{512 y ^{6}}{x ^{\frac{3}{2}}}

= \frac{\frac{512 y ^{6}}{x ^{\frac{3}{2}}}}{( 4 x ^{\frac{2}{3}} y ^{- \frac{1}{4}} ) ^{3}}

Vereinfache

(4 x^{\frac{2}{3}} y^{- \frac{1}{4}})^{3} : \frac{64 x ^{2}}{y ^{\frac{3}{4}}}

= \frac{\frac{512 y ^{6}}{x ^{\frac{3}{2}}}}{\frac{64 x ^{2}}{y ^{\frac{3}{4}}}}

Teile Brüche:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{512 y ^{6} y ^{\frac{3}{4}}}{x ^{\frac{3}{2}} \cdot 64 x ^{2}}

Teile die Zahlen:

\frac{512}{64} = 8

= \frac{8 y ^{6} y ^{\frac{3}{4}}}{x ^{2} x ^{\frac{3}{2}}}

8 y^{6} y^{\frac{3}{4}} = 8 y^{6 + \frac{3}{4}}

= \frac{8 y ^{\frac{3}{4} + 6}}{x ^{2} x ^{\frac{3}{2}}}

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

= \frac{8 y ^{\frac{3}{4} + 6}}{x ^{2 + \frac{3}{2}}}

x^{2 + \frac{3}{2}} = x^{\frac{7}{2}}

= \frac{8 y ^{\frac{3}{4} + 6}}{x ^{\frac{7}{2}}}

y^{6 + \frac{3}{4}} = y^{\frac{27}{4}}

= \frac{8 y ^{\frac{27}{4}}}{x ^{\frac{7}{2}}}

12 x^{2} + 17 x = 5

\frac{3 x - 2}{7} = \frac{6 x - 5}{13}

x + 5 < 20

x^{2} + 3 x - 54 < 0

∣ 5 x - 7 ∣ \leq 3