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Popular >

factorizar 3(3/20)^{1/3}-5(3/20)^{4/3}

Solución

factorizar

3 (\frac{3}{20})^{\frac{1}{3}} - 5 (\frac{3}{20})^{\frac{4}{3}}

Solución

\frac{9 \cdot 3 ^{\frac{1}{3}}}{4 \cdot 2 0 ^{\frac{1}{3}}}

+1

Notación decimal

1.19549 \dots

Pasos de solución

3 (\frac{3}{20})^{\frac{1}{3}} - 5 (\frac{3}{20})^{\frac{4}{3}}

Aplicar las leyes de los exponentes:

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

(\frac{3}{20})^{\frac{4}{3}} = (\frac{3}{20})^{1 + \frac{1}{3}} = (\frac{3}{20})^{1} (\frac{3}{20})^{\frac{1}{3}}

= 3 (\frac{3}{20})^{\frac{1}{3}} - 5 (\frac{3}{20})^{1} (\frac{3}{20})^{\frac{1}{3}}

Factorizar el termino común

(\frac{3}{20})^{\frac{1}{3}}

= (\frac{3}{20})^{\frac{1}{3}} (3 - 5 \cdot \frac{3}{20})

Simplificar

= (\frac{3}{20})^{\frac{1}{3}} (- \frac{3}{4} + 3)

Simplificar

3 - \frac{3}{4}

en una fracción:

\frac{9}{4}

= \frac{9}{4} (\frac{3}{20})^{\frac{1}{3}}

Multiplicar fracciones:

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

= \frac{9 ( \frac{3}{20} ) ^{\frac{1}{3}}}{4}

(\frac{3}{20})^{\frac{1}{3}} = \frac{3 ^{\frac{1}{3}}}{2 0 ^{\frac{1}{3}}}

= \frac{9 \cdot \frac{3 ^{\frac{1}{3}}}{2 0 ^{\frac{1}{3}}}}{4}

Multiplicar

9 \cdot \frac{3 ^{\frac{1}{3}}}{2 0 ^{\frac{1}{3}}} : \frac{9 \cdot 3 ^{\frac{1}{3}}}{2 0 ^{\frac{1}{3}}}

= \frac{\frac{9 \cdot 3 ^{\frac{1}{3}}}{2 0 ^{\frac{1}{3}}}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{3 ^{\frac{1}{3}} \cdot 9}{2 0 ^{\frac{1}{3}} \cdot 4}

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