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simplificar (1.2)0.3^{-0.25}0.9^{-0.75}

Solución

simplificar

(1.2) \cdot 0. 3^{- 0.25} \cdot 0. 9^{- 0.75}

\frac{6}{5 \cdot 0. 3 ^{0.25} \cdot 0. 9 ^{0.75}}

Notación decimal

1.75476 \dots

Pasos de solución

(1.2) \cdot 0. 3^{- 0.25} \cdot 0. 9^{- 0.75}

Aplicar la propiedad:

(a) = a

(1.2) = 1.2

= 1.2 \cdot 0. 3^{- 0.25} \cdot 0. 9^{- 0.75}

Aplicar las leyes de los exponentes:

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

0. 3^{- 0.25} = \frac{1}{0. 3 ^{0.25}}

= 1.2 \cdot \frac{1}{0. 3 ^{0.25}} \cdot 0. 9^{- 0.75}

Aplicar las leyes de los exponentes:

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

0. 9^{- 0.75} = \frac{1}{0. 9 ^{0.75}}

= 1.2 \cdot \frac{1}{0. 3 ^{0.25}} \cdot \frac{1}{0. 9 ^{0.75}}

1.2 \cdot \frac{1}{0. 3 ^{0.25}} \cdot \frac{1}{0. 9 ^{0.75}} = \frac{1.2}{0. 3 ^{0.25} \cdot 0. 9 ^{0.75}}

= \frac{1.2}{0. 3 ^{0.25} \cdot 0. 9 ^{0.75}}

\frac{1.2}{0. 3 ^{0.25} \cdot 0. 9 ^{0.75}} = \frac{12}{10 \cdot 0. 3 ^{0.25} \cdot 0. 9 ^{0.75}}

= \frac{12}{10 \cdot 0. 3 ^{0.25} \cdot 0. 9 ^{0.75}}

Descomponer el número en factores primos:

12 = 2 \cdot 6

= \frac{2 \cdot 6}{10 \cdot 0. 3 ^{0.25} \cdot 0. 9 ^{0.75}}

Descomponer el número en factores primos:

10 = 2 \cdot 5

= \frac{2 \cdot 6}{2 \cdot 5 \cdot 0. 3 ^{0.25} \cdot 0. 9 ^{0.75}}

Eliminar los terminos comunes:

2

= \frac{6}{5 \cdot 0. 3 ^{0.25} \cdot 0. 9 ^{0.75}}

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

(6.83 \cdot 1 0^{- 6}) \cdot (3.2 \cdot 1 0^{- 4})^{'}

δ (x - x^{0}) e^{- 10 x}

1.6 x (1 + 0.018848)^{- 3}