Matemática discreta Ejemplos

$p = 5.67 \cdot \frac{10^{- 8} W}{m^{2} K^{4}} \cdot (0.06 m^{2}) \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 1

Simplifica el numerador.

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Paso 1.1

Reescribe la expresión mediante la regla del exponente negativo $b^{- n} = \frac{1}{b^{n}}$ .

$p = 5.67 \cdot \frac{\frac{1}{10^{8}} W}{m^{2} K^{4}} \cdot (0.06 m^{2}) \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 1.2

Eleva $10$ a la potencia de $8$ .

$p = 5.67 \cdot \frac{\frac{1}{100000000} W}{m^{2} K^{4}} \cdot (0.06 m^{2}) \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 2

Combina $\frac{1}{100000000}$ y $W$ .

$p = 5.67 \cdot \frac{\frac{W}{100000000}}{m^{2} K^{4}} \cdot (0.06 m^{2}) \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 3

Multiplica el numerador por la recíproca del denominador.

$p = 5.67 \cdot (\frac{W}{100000000} \cdot \frac{1}{m^{2} K^{4}}) \cdot (0.06 m^{2}) \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 4

Combinar.

$p = 5.67 \cdot \frac{W \cdot 1}{100000000 (m^{2} K^{4})} \cdot (0.06 m^{2}) \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 5

Multiplica $W$ por $1$ .

$p = 5.67 \cdot \frac{W}{100000000 (m^{2} K^{4})} \cdot (0.06 m^{2}) \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 6

Combina $5.67$ y $\frac{W}{100000000 m^{2} K^{4}}$ .

$p = \frac{5.67 W}{100000000 m^{2} K^{4}} \cdot (0.06 m^{2}) \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 7

Reescribe con la propiedad conmutativa de la multiplicación.

$p = 0.06 \frac{5.67 W}{100000000 m^{2} K^{4}} m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 8

Factoriza $5.67$ de $5.67 W$ .

$p = 0.06 \frac{5.67 (W)}{100000000 m^{2} K^{4}} m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 9

Factoriza $100000000$ de $100000000 m^{2} K^{4}$ .

$p = 0.06 \frac{5.67 (W)}{100000000 (m^{2} K^{4})} m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 10

Separa las fracciones.

$p = 0.06 (\frac{5.67}{100000000} \cdot \frac{W}{m^{2} K^{4}}) m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 11

Divide $5.67$ por $100000000$ .

$p = 0.06 (0.00000005 \frac{W}{m^{2} K^{4}}) m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 12

Combina $0.00000005$ y $\frac{W}{m^{2} K^{4}}$ .

$p = 0.06 \frac{0.00000005 W}{m^{2} K^{4}} m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 13

Multiplica $0.06 \frac{0.00000005 W}{m^{2} K^{4}}$ .

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Paso 13.1

Combina $0.06$ y $\frac{0.00000005 W}{m^{2} K^{4}}$ .

$p = \frac{0.06 (0.00000005 W)}{m^{2} K^{4}} m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 13.2

Multiplica $0.00000005$ por $0.06$ .

$p = \frac{0 W}{m^{2} K^{4}} m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 14

Cancela el factor común de $m^{2}$ .

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Paso 14.1

Factoriza $m^{2}$ de $m^{2} K^{4}$ .

$p = \frac{0 W}{m^{2} (K^{4})} m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 14.2

Cancela el factor común.

$p = \frac{0 W}{m^{2} K^{4}} m^{2} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 14.3

Reescribe la expresión.

$p = \frac{0 W}{K^{4}} \cdot ({284.38}^{4} - {282.15}^{4})$

Paso 15

Simplifica cada término.

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Paso 15.1

Eleva $284.38$ a la potencia de $4$ .

$p = \frac{0 W}{K^{4}} \cdot (6540277860.79384 - {282.15}^{4})$

Paso 15.2

Eleva $282.15$ a la potencia de $4$ .

$p = \frac{0 W}{K^{4}} \cdot (6540277860.79384 - 1 \cdot 6337532776.3475)$

Paso 15.3

Multiplica $- 1$ por $6337532776.3475$ .

$p = \frac{0 W}{K^{4}} \cdot (6540277860.79384 - 6337532776.3475)$

Paso 16

Resta $6337532776.3475$ de $6540277860.79384$ .

$p = \frac{0 W}{K^{4}} \cdot 202745084.44634$

Paso 17

Multiplica $\frac{0 W}{K^{4}} \cdot 202745084.44634$ .

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Paso 17.1

Combina $\frac{0 W}{K^{4}}$ y $202745084.44634$ .

$p = \frac{0 W \cdot 202745084.44634}{K^{4}}$

Paso 17.2

Multiplica $202745084.44634$ por $0$ .

$p = \frac{0.68973877 W}{K^{4}}$