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simplificar (-20(m^2v)(-v)^3)/(5(-v)^2(-m^4))

Solución

simplificar

\frac{- 20 ( m ^{2} v ) ( - v ) ^{3}}{5 ( - v ) ^{2} ( - m ^{4} )}

- \frac{4 v ^{2}}{m ^{2}}

Pasos de solución

\frac{- 20 ( m ^{2} v ) ( - v ) ^{3}}{5 ( - v ) ^{2} ( - m ^{4} )}

Aplicar la propiedad:

a (- b) = - ab

5 (- v)^{2} (- m^{4}) = - 5 (- v)^{2} m^{4}

= \frac{- 20 m ^{2} v ( - v ) ^{3}}{- 5 ( - v ) ^{2} m ^{4}}

Simplificar

- 20 m^{2} v (- v)^{3} : 20 m^{2} v^{4}

= \frac{20 m ^{2} v ^{4}}{- 5 ( - v ) ^{2} m ^{4}}

Descomponer el número en factores primos:

20 = 5 \cdot 4

= \frac{5 \cdot 4 m ^{2} v ^{4}}{- 5 ( - v ) ^{2} m ^{4}}

Eliminar los terminos comunes:

5

= \frac{4 m ^{2} v ^{4}}{- ( - v ) ^{2} m ^{4}}

Simplificar

\frac{m ^{2}}{m ^{4}} : \frac{1}{m ^{2}}

= \frac{4 v ^{4}}{- ( - v ) ^{2} m ^{2}}

Aplicar las leyes de los exponentes:

(- a)^{n} = a^{n},

n

es par

(- v)^{2} = v^{2}

= \frac{4 v ^{4}}{- v ^{2} m ^{2}}

Simplificar

\frac{v ^{4}}{v ^{2}} : v^{2}

= \frac{4 v ^{2}}{- m ^{2}}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{4 v ^{2}}{m ^{2}}

s (s + 1)^{2}

\frac{x ^{2} - 81}{4 x ^{3} - 36 x ^{2}}

\frac{8 x ^{3}}{24 x ^{2} + 24 x}

1 - 1728 y^{6}

- \frac{1}{25}