simplificar 4pi(8.85(10)^{-12})(34)^2(1/100)^2

Solución

simplificar

4 π (8.85 (10)^{- 12}) (34)^{2} (\frac{1}{100})^{2}

1.28562 E - 11

Pasos de solución

4 π (8.85 (10)^{- 12}) (34)^{2} (\frac{1}{100})^{2}

Aplicar las leyes de los exponentes:

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

= 3 4^{2} \cdot 4 \cdot 8.85 π (\frac{1}{100})^{2} \frac{1}{1 0 ^{12}}

(\frac{1}{100})^{2} = \frac{1}{10 0 ^{2}}

= 3 4^{2} \cdot 4 \cdot 8.85 π \frac{1}{1 0 ^{12}} \cdot \frac{1}{10 0 ^{2}}

Multiplicar fracciones:

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

= 8.85 \cdot \frac{3 4 ^{2} \cdot 1 \cdot 1 \cdot 4 π}{1 0 ^{12} \cdot 10 0 ^{2}}

\frac{1 \cdot 1 \cdot 4 π 3 4 ^{2}}{1 0 ^{12} \cdot 10 0 ^{2}} = \frac{289 π}{5 ^{16} \cdot 4096}

= 8.85 \cdot \frac{289 π}{5 ^{16} \cdot 4096}

Multiplicar fracciones:

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

= \frac{289 π 8.85}{5 ^{16} \cdot 4096}

Multiplicar los numeros:

289 \cdot 8.85 = 2557.65

= \frac{2557.65 π}{5 ^{16} \cdot 4096}

Convertir el elemento a una forma decimal

5^{16} = 152587890625

= \frac{2557.65 π}{152587890625 \cdot 4096}

Multiplicar los numeros:

2557.65 \cdot 3.14159 \dots = 8035.09445 \dots

= \frac{8035.09445 \dots}{152587890625 \cdot 4096}

Multiplicar los numeros:

152587890625 \cdot 4096 = 6.25 E 14

= \frac{8035.09445 \dots}{6.25 E 14}

Dividir:

\frac{8035.09445 \dots}{6.25 E 14} = 1.28562 E - 11

= 1.28562 E - 11

10 e^{- \frac{1}{( 108 \cdot 0.01 )}}

(3 r^{3} s^{5} t) (7 r^{3} s^{5} t)

\frac{- 70}{10}