Então o valor de A+B?

por Drufox Sex 27 Jul 2012, 19:47

Analise as expressões abaixo
$A=\sqrt[3]{\frac{(0,005)^2.(0,000075))}{10}}$

$b= [\frac{(5.10^-^4).(2^-^1^/^3)}{3^-^1^/^3}]$

Então o valor de A+B?

por danjr5 Sex 27 Jul 2012, 20:45

Calculando A:

$A = \sqrt[3]{\frac{\left ( \frac{5}{10^3} \right )^2 \times \frac{75}{10^6}}{10}} \\\\\\ A = \sqrt[3]{\frac{\frac{5^2}{10^6} \times \frac{3 \times 5^2}{10^6}}{10}} \\\\\\ A = \sqrt[3]{\frac{3 \times 5^4}{10^{13}}} \\\\\\ \boxed{A = \frac{5}{10000} \times \sqrt[3]{\frac{3}{2}}}$

Calculando B:

$B = \frac{5 \times 10^{- 4} \times \frac{1}{\sqrt[3]{2}}}{\frac{1}{\sqrt[3]{3}}} \\\\\\ B = 5 \times 10^{- 4} \times \frac{1}{\sqrt[3]{2}} \times \sqrt[3]{3} \\\\\\ \boxed{B = \frac{5}{10000} \times \sqrt[3]{\frac{3}{2}}}$

Note que $A = B$ , então

$A + B = \\\\ 2A = \\\\ \frac{10}{10000}\sqrt[3]{\frac{3}{2}} = \\\\\\ \boxed{\frac{1}{1000}\sqrt[3]{\frac{3}{2}}}$

por Drufox Sex 27 Jul 2012, 21:04

a resposta é 0 !
ou olha (0,005)²=[5.10^(-3) ]² =[5².10^(-6)] eu não entendi o porque do -6
não teria que ser [5².10^(-9)]

por danjr5 Sex 27 Jul 2012, 21:28

Drufox,

$[5 \times 10^{- 3}]^2 = \\\\ (5 \times 10^{- 3}) \times (5 \times 10^{- 3}) = \\\\ 5^2 \times 10^{[- 3 + (- 3)]} = \\\\ 5^2 \times 10^{- 3 - 3} = \\\\ \boxed{5^2 \times 10^{- 6}}$