Question

Calcule o valor da expressão:

$\frac{(0.0000045)\times (0.0032)\times (0.00125)}{(0.002){}^{4}\times (0.0003) {}^{2}\times (0.05){}^{2}}$
A resposta final deve ser:
$5 \times 10 {}^{9}$

Answer 1

Oi, vou converter os valores em notação científica pra facilitar.

$\frac{(0.0000045)\times (0.0032)\times (0.00125)}{(0.002){}^{4}\times (0.0003) {}^{2}\times (0.05){}^{2}}$ 

(4.5*10^-5 * 3.2*10^-3 *1.25*10^-3) / (2*10^-3)^4 * (3*10^-4)^2 * (5*10^-2)^2 [/tex]

Simplificando a notação a parte de cima primeiro:

$4.5*10^{-5} * 3.2*10^{-3} * 1.25*10^{-3}$
$4.5* 3.2 * 1.25 * 10^{-5} * 10^{-3} * 10^{-3}$
$4.5 * 3.2 * 1.25 * 10^{-11}$

Agora da parte de baixo:

{(2*10^{-3})}^4 * {(3*10^{-4})}^2 * {(5*10^{-2})}^2
(16*10^{-12}) * (9*10^{-8}) * (25*10^{-4})[/tex]
 16*10^{-12} * 9 * 10^{-8} * 25 * 10^{-4}
 16*9 * 25 * 10^{-4} * 10^{-12} * 10^{-8}
 16*9 * 25 * 10^{-24}

Então temos:

$\frac{16 * 9 * 25 * 10^{-24}}{4.5 * 3.2 * 1.25 * 10^{-11}}$
$\frac{16 * 2 * 25 * 10^{-24}}{3.2 * 1.25 * 10^{-11}}$
$\frac{32 * 25 * 10^{-24}}{3.2 * 1.25 * 10^{-11}}$
$\frac{10 * 25 * 10^{-24}}{1.25 * 10^{-11}}$
$\frac{25 * 10^{-23}}{1.25 * 10^{-11}}$
$\frac{2 * 10^{-22}}{10^{-11}}$

Desculpa, mas no final da minha conta deu 2 * 10^-11 :/

Answer 2

vamos calcular separado, 

$0,0000045=4,5.10^{-6 } \\ 0,0032=3,2.10^{-3} \\ 0,00125=1,25.10^{-3} \\ \\ (4,5\times3,2\times1,25)(10^{-6-3-3})= \\ \\ 18.10^{-12}  denominador [tex](0,002)^4=(2.10^{-3})^4=16.10^{-12} \\ (0,0003)^2=(3.10^{-4})^2=9.10^{-8} \\ (0,05)^2=(5.10^{-2})^2=25.10^{-4} \\ \\ (16\times9\times25)(10^{-12-8-4})= \\ 3600.10^{-24}$

vamos ao exercício que será

$18.10^{-12}\div3600.10^{-24}= \\ \\ (18\div3600)(10^{-12-(-24)}= \\ \\ 0,005.10^{-12+24}= \\ \\ 0,005.10^{12}= \\ \\ 5.10^{-3}.10^{12}= \\ \\ 5.10^{-3+12}= \\ \\ \fbox{ 5.10^9 }$