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simplificar 1.610^{-19}910^96.610^{-6}(1/(5sqrt(2))-1/5)

Solución

simplificar

1.6 \cdot 1 0^{- 19} \cdot 9 \cdot 1 0^{9} \cdot 6.6 \cdot 1 0^{- 6} \cdot (\frac{1}{5 2} - \frac{1}{5})

- 5.56731 E - 16

Pasos de solución

1.6 \cdot 1 0^{- 19} \cdot 9 \cdot 1 0^{9} \cdot 6.6 \cdot 1 0^{- 6} (\frac{1}{5 2} - \frac{1}{5})

Aplicar las leyes de los exponentes:

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

= 1 0^{- 6} \cdot 1 0^{9} \cdot 9 \cdot 1.6 \cdot 6.6 \cdot \frac{1}{1 0 ^{19}} (\frac{1}{5 2} - \frac{1}{5})

Aplicar las leyes de los exponentes:

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

= 1 0^{9} \cdot 9 \cdot 1.6 \cdot 6.6 \cdot \frac{1}{1 0 ^{6}} \cdot \frac{1}{1 0 ^{19}} (\frac{1}{5 2} - \frac{1}{5})

Multiplicar fracciones:

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

= 1.6 \cdot 6.6 \cdot \frac{1 0 ^{9} \cdot 1 \cdot 1 \cdot 9 ( \frac{1}{5 2} - \frac{1}{5} )}{1 0 ^{19} \cdot 1 0 ^{6}}

\frac{1 \cdot 1 \cdot 9 \cdot 1 0 ^{9} ( \frac{1}{5 2} - \frac{1}{5} )}{1 0 ^{19} \cdot 1 0 ^{6}} = \frac{9 ( 1 - 2 )}{5 ^{17} \cdot 65536 2}

= 1.6 \cdot 6.6 \cdot \frac{9 ( 1 - 2 )}{5 ^{17} \cdot 65536 2}

Multiplicar los numeros:

1.6 \cdot 6.6 = 10.56

= 10.56 \cdot \frac{9 ( 1 - 2 )}{5 ^{17} \cdot 65536 2}

Multiplicar fracciones:

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

= \frac{9 ( 1 - 2 ) \cdot 10.56}{5 ^{17} \cdot 65536 2}

Multiplicar los numeros:

9 \cdot 10.56 = 95.04

= \frac{95.04 ( 1 - 2 )}{5 ^{17} \cdot 65536 2}

Convertir el elemento a una forma decimal

5^{17} = 762939453125

= \frac{95.04 ( 1 - 2 )}{762939453125 \cdot 65536 2}

Convertir el elemento a una forma decimal

2 = 1.41421 \dots

= \frac{95.04 ( 1 - 2 )}{762939453125 \cdot 65536 \cdot 1.41421 \dots}

Multiplicar los numeros:

762939453125 \cdot 65536 \cdot 1.41421 \dots = 7.07107 E 16

= \frac{95.04 ( 1 - 2 )}{7.07107 E 16}

Dividir:

\frac{95.04}{7.07107 E 16} = 1.34407 E - 15

= 1.34407 E - 15 (1 - 2)

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 1.34407 E - 15, b = 1, c = 2

= 1.34407 E - 15 \cdot 1 - 1.34407 E - 152

= 1 \cdot 1.34407 E - 15 - 2 \cdot 1.34407 E - 15

Simplificar

1 \cdot 1.34407 E - 15 - 2 \cdot 1.34407 E - 15 : - 5.56731 E - 16

= - 5.56731 E - 16

(6 x^{5}) x (3 y^{3} + 2)

0.106 \cdot 20 \cdot 1 0^{- 3}

1.4 \cdot 1 0^{- 20}

142 e^{- 0.12602 (10)}