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Popular Álgebra >

simplificar (x^{-4}+x^2y^{-3})/((xy)^{-2)}

Solução

simplificar

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

Solução

\frac{y ^{3} + x ^{6}}{x ^{2} y}

Passos da solução

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

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

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

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

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

Aplicar as propriedades das frações:

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

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

Simplificar

x^{- 4} + \frac{x ^{2}}{y ^{3}}

em uma fração:

\frac{y ^{3} + x ^{6}}{x ^{4} y ^{3}}

= \frac{\frac{x ^{6} + y ^{3}}{x ^{4} y ^{3}} x ^{2} y ^{2}}{1}

Aplicar as propriedades das frações:

\frac{a}{1} = a

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

Multiplicar frações:

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

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

Aplicar as propriedades dos expoentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{x ^{2}}{x ^{4}} = \frac{1}{x ^{4 - 2}}

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

Subtrair:

4 - 2 = 2

= \frac{y ^{2} ( x ^{6} + y ^{3} )}{x ^{2} y ^{3}}

Aplicar as propriedades dos expoentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{y ^{2}}{y ^{3}} = \frac{1}{y ^{3 - 2}}

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

Subtrair:

3 - 2 = 1

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

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