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Popular >

simplificar (3^{-6}*16^{3/2})^{1/6}

Solución

simplificar

(3^{- 6} \cdot 1 6^{\frac{3}{2}})^{\frac{1}{6}}

\frac{2}{3}

Decimal

0.66666 \dots

Pasos de solución

(3^{- 6} \cdot 1 6^{\frac{3}{2}})^{\frac{1}{6}}

Aplicar las leyes de los exponentes:

(a \cdot b)^{n} = a^{n} b^{n}

(3^{- 6} \cdot 1 6^{\frac{3}{2}})^{\frac{1}{6}} = (3^{- 6})^{\frac{1}{6}} (1 6^{\frac{3}{2}})^{\frac{1}{6}}

= (3^{- 6})^{\frac{1}{6}} (1 6^{\frac{3}{2}})^{\frac{1}{6}}

(3^{- 6})^{\frac{1}{6}} = \frac{1}{3}

= \frac{1}{3} (1 6^{\frac{3}{2}})^{\frac{1}{6}}

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}, a \geq 0

(1 6^{\frac{3}{2}})^{\frac{1}{6}} = 1 6^{\frac{3}{2} \cdot \frac{1}{6}}

= \frac{1}{3} \cdot 1 6^{\frac{3}{2} \cdot \frac{1}{6}}

\frac{3}{2} \cdot \frac{1}{6} = \frac{1}{4}

= \frac{1}{3} \cdot 1 6^{\frac{1}{4}}

Descomponer el número en factores primos:

16 = 2^{4}

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

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}, a \geq 0

(2^{4})^{\frac{1}{4}} = 2^{4 \cdot \frac{1}{4}}

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

4 \cdot \frac{1}{4} = 1

= \frac{1}{3} \cdot 2^{1}

Aplicar las leyes de los exponentes:

a^{1} = a

2^{1} = 2

= \frac{1}{3} \cdot 2

\frac{1}{3} \cdot 2 = \frac{2}{3}

= \frac{2}{3}

- \frac{7}{4} - 1

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

x (x + 16) = - 64

p^{2} - 7 p + 3 = 0

\frac{5 x + 10}{x - 1} < 0