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simplificar 10^{-(5/(-0.085))}*31000^{1/(-0.085)}

Solución

simplificar

1 0^{- (\frac{5}{- 0.085})} \cdot 3100 0^{\frac{1}{- 0.085}}

963784.79965 \dots

Pasos de solución

1 0^{- (\frac{5}{- 0.085})} \cdot 3100 0^{\frac{1}{- 0.085}}

Aplicar las leyes de los exponentes:

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

= 3100 0^{\frac{1}{- 0.085}} \cdot \frac{1}{1 0 ^{\frac{5}{- 0.085}}}

\frac{1}{1 0 ^{\frac{5}{- 0.085}}} = 1 0^{\frac{5}{0.085}}

= 3100 0^{\frac{1}{- 0.085}} \cdot 1 0^{\frac{5}{0.085}}

Aplicar las propiedades de las fracciones:

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

= 3100 0^{- \frac{1}{0.085}} \cdot 1 0^{\frac{5}{0.085}}

Factorizar entero

10 = 2 \cdot 5

= (2 \cdot 5)^{\frac{5}{0.085}} \cdot 3100 0^{- \frac{1}{0.085}}

Aplicar las leyes de los exponentes:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{\frac{5}{0.085}} = 2^{\frac{5}{0.085}} \cdot 5^{\frac{5}{0.085}}

= 2^{\frac{5}{0.085}} \cdot 5^{\frac{5}{0.085}} \cdot 3100 0^{- \frac{1}{0.085}}

Factorizar entero

31000 = 2^{3} \cdot 5^{3} \cdot 31

= 2^{\frac{5}{0.085}} \cdot 5^{\frac{5}{0.085}} (2^{3} \cdot 5^{3} \cdot 31)^{- \frac{1}{0.085}}

Aplicar las leyes de los exponentes:

(ab)^{c} = a^{c} b^{c}

(2^{3} \cdot 5^{3} \cdot 31)^{- \frac{1}{0.085}} = (2^{3})^{- \frac{1}{0.085}} (5^{3})^{- \frac{1}{0.085}} \cdot 3 1^{- \frac{1}{0.085}}

= 2^{\frac{5}{0.085}} \cdot 5^{\frac{5}{0.085}} (2^{3})^{- \frac{1}{0.085}} (5^{3})^{- \frac{1}{0.085}} \cdot 3 1^{- \frac{1}{0.085}}

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}

(2^{3})^{- \frac{1}{0.085}} = 2^{3 (- \frac{1}{0.085})}, (5^{3})^{- \frac{1}{0.085}} = 5^{3 (- \frac{1}{0.085})}

= 2^{\frac{5}{0.085}} \cdot 5^{\frac{5}{0.085}} \cdot 2^{3 (- \frac{1}{0.085})} \cdot 5^{3 (- \frac{1}{0.085})} \cdot 3 1^{- \frac{1}{0.085}}

Simplificar

= 2^{\frac{5}{0.085}} \cdot 5^{\frac{5}{0.085}} \cdot 2^{- 35.29411 \dots} \cdot 5^{- 35.29411 \dots} \cdot 3 1^{- \frac{1}{0.085}}

Aplicar las leyes de los exponentes:

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

2^{\frac{5}{0.085}} \cdot 2^{- 35.29411 \dots} = 2^{\frac{5}{0.085} - 35.29411 \dots}

= 5^{\frac{5}{0.085}} \cdot 2^{\frac{5}{0.085} - 35.29411 \dots} \cdot 5^{- 35.29411 \dots} \cdot 3 1^{- \frac{1}{0.085}}

Aplicar las leyes de los exponentes:

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

5^{\frac{5}{0.085}} \cdot 5^{- 35.29411 \dots} = 5^{\frac{5}{0.085} - 35.29411 \dots}

= 2^{\frac{5}{0.085} - 35.29411 \dots} \cdot 5^{\frac{5}{0.085} - 35.29411 \dots} \cdot 3 1^{- \frac{1}{0.085}}

2^{\frac{5}{0.085} - 35.29411 \dots} = 2^{23.52941 \dots}

= 2^{23.52941 \dots} \cdot 3 1^{- \frac{1}{0.085}} \cdot 5^{\frac{5}{0.085} - 35.29411 \dots}

5^{\frac{5}{0.085} - 35.29411 \dots} = 5^{23.52941 \dots}

= 2^{23.52941 \dots} \cdot 5^{23.52941 \dots} \cdot 3 1^{- \frac{1}{0.085}}

Aplicar las leyes de los exponentes:

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

3 1^{- \frac{1}{0.085}} = \frac{1}{3 1 ^{\frac{1}{0.085}}}

= 2^{23.52941 \dots} \cdot 5^{23.52941 \dots} \cdot \frac{1}{3 1 ^{\frac{1}{0.085}}}

Multiplicar fracciones:

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

= \frac{1 \cdot 2 ^{23.52941 \dots} \cdot 5 ^{23.52941 \dots}}{3 1 ^{\frac{1}{0.085}}}

Multiplicar:

1 \cdot 2^{23.52941 \dots} = 2^{23.52941 \dots}

= \frac{2 ^{23.52941 \dots} \cdot 5 ^{23.52941 \dots}}{3 1 ^{\frac{1}{0.085}}}

3 1^{\frac{1}{0.085}} = 3.51101 E 17

= \frac{2 ^{23.52941 \dots} \cdot 5 ^{23.52941 \dots}}{3.51101 E 17}

2^{23.52941 \dots} = 12107618.31119 \dots

= \frac{5 ^{23.52941 \dots} \cdot 12107618.31119 \dots}{3.51101 E 17}

5^{23.52941 \dots} = 2.79481 E 16

= \frac{2.79481 E 16 \cdot 12107618.31119 \dots}{3.51101 E 17}

Multiplicar los numeros:

12107618.31119 \dots \cdot 2.79481 E 16 = 3.38386 E 23

= \frac{3.38386 E 23}{3.51101 E 17}

Dividir:

\frac{3.38386 E 23}{3.51101 E 17} = 963784.79965 \dots

= 963784.79965 \dots

(2.84758 \cdot 1 0^{9}) (1.6022 \cdot 1 0^{- 19})

2 \cdot π \cdot 8.85 \cdot 1 0^{- 12} \cdot \frac{10000}{ln ( 1.2 )}

0.3 \cdot 19 \cdot 1 0^{- 6} \cdot 55

2.15 \cdot 1 0^{- 2} \cdot 1.2

(3 x^{\frac{9}{2}} y^{\frac{3}{5}}) (9 x^{\frac{9}{2}} y)