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simplificar (15q^6+5q^2)(5q^4)^{-1}

Solución

simplificar

(15 q^{6} + 5 q^{2}) (5 q^{4})^{- 1}

\frac{3 q ^{4} + 1}{q ^{2}}

Pasos de solución

(15 q^{6} + 5 q^{2}) (5 q^{4})^{- 1}

Aplicar las leyes de los exponentes:

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

(5 q^{4})^{- 1} = \frac{1}{5 q ^{4}}

= (15 q^{6} + 5 q^{2}) \frac{1}{5 q ^{4}}

Aplicar las propiedades de las fracciones:

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

= \frac{( 15 q ^{6} + 5 q ^{2} ) \cdot 1}{5 q ^{4}}

Aplicar la propiedad:

a \cdot 1 = a

(15 q^{6} + 5 q^{2}) \cdot 1 = (15 q^{6} + 5 q^{2})

= \frac{15 q ^{6} + 5 q ^{2}}{5 q ^{4}}

Factorizar

15 q^{6} + 5 q^{2} : 5 q^{2} (3 q^{4} + 1)

= \frac{5 q ^{2} ( 3 q ^{4} + 1 )}{5 q ^{4}}

Eliminar los terminos comunes:

5

= \frac{q ^{2} ( 3 q ^{4} + 1 )}{q ^{4}}

Aplicar las leyes de los exponentes:

a^{b + c} = a^{b} \cdot a^{c}

q^{4} = q^{2} q^{2}

= \frac{q ^{2} ( 3 q ^{4} + 1 )}{q ^{2} q ^{2}}

Eliminar los terminos comunes:

q^{2}

= \frac{3 q ^{4} + 1}{q ^{2}}

\frac{1}{x - \frac{x}{x - \frac{x ^{2}}{x + 1}}}

(5 x y + 7 z + 12 x) + (6 x - 8 z + 4 x y) - (3 z - 15 x y)

(a + b) (x + y)

1.5 \times 2

\frac{4}{7 - 5}