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Popular Álgebra >

simplificar 5x 1/56 x(6.022x10^{23})/1

Solução

simplificar

5 x \frac{1}{56} x \frac{6.022 x 1 0 ^{23}}{1}

Solução

\frac{3011 \cdot 2 ^{18} \cdot 5 ^{21} x ^{3}}{7}

Passos da solução

5 x \frac{1}{56} x \frac{6.022 x \cdot 1 0 ^{23}}{1}

Aplicar as propriedades das frações:

\frac{a}{1} = a

\frac{6.022 x \cdot 1 0 ^{23}}{1} = 6.022 x \cdot 1 0^{23}

= 5 x \frac{1}{56} x \cdot 6.022 x \cdot 1 0^{23}

6.022 = \frac{3011}{500}

= 5 x \frac{1}{56} x \frac{3011}{500} x \cdot 1 0^{23}

Aplicar as propriedades das frações:

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

= \frac{5 x \cdot 1 \cdot x \cdot 3011 x \cdot 1 0 ^{23}}{56 \cdot 500}

Multiplicar os números:

56 \cdot 500 = 28000

= \frac{5 x \cdot 1 \cdot x \cdot 3011 x \cdot 1 0 ^{23}}{28000}

Simplificar

5 x \cdot 1 \cdot x \cdot 3011 x \cdot 1 0^{23} : 15055 x^{3} \cdot 1 0^{23}

= \frac{15055 x ^{3} \cdot 1 0 ^{23}}{28000}

Fatorar o número:

15055 = 5 \cdot 3011

= \frac{5 \cdot 3011 x ^{3} \cdot 1 0 ^{23}}{28000}

Fatorar o número:

28000 = 5 \cdot 5600

= \frac{5 \cdot 3011 x ^{3} \cdot 1 0 ^{23}}{5 \cdot 5600}

Eliminar o fator comum:

5

= \frac{3011 x ^{3} \cdot 1 0 ^{23}}{5600}

Fatorar

5600 : 1 0^{2} \cdot 56

= \frac{3011 x ^{3} \cdot 1 0 ^{23}}{1 0 ^{2} \cdot 56}

\frac{1 0 ^{23}}{1 0 ^{2}} = 1 0^{21}

= \frac{3011 x ^{3} \cdot 1 0 ^{21}}{56}

Fatorar

1 0^{21} : 2^{21} \cdot 5^{21}

= \frac{3011 x ^{3} \cdot 2 ^{21} \cdot 5 ^{21}}{56}

Fatorar

56 : 2^{3} \cdot 7

= \frac{3011 x ^{3} \cdot 2 ^{21} \cdot 5 ^{21}}{2 ^{3} \cdot 7}

\frac{2 ^{21}}{2 ^{3}} = 2^{18}

= \frac{3011 x ^{3} \cdot 2 ^{18} \cdot 5 ^{21}}{7}

= \frac{3011 \cdot 2 ^{18} \cdot 5 ^{21} x ^{3}}{7}

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