Question

d)( 5x 10^3)x 7x 10^2) =                                                                                                           e)(12 x 10^2) :(4 x 10^2)=                                                                                                       f)(3x 10^3):(6x 10^3)

Answer 1

d) 5 . 10³ . 7 . 10²
5 . 1000 . 7 .100
5000 . 700
3500000

e) 12.10² : 4 . 10²
12. 100 :4 .100
1200 : 400
3

f) 3. 10³ : 6 . 10³
3 .1000 :6 . 1000
3000 :6000
1/2

Answer 2

$(a*b)*c*d=a*b*c*d$

Multiplicação de potências de mesma base: Repete-se a base e soma-se os expoentes

$x^{a}*x^{b}=x^{a+b}$

Razão entre potências de mesma base: Repete-se a base e subtrai-se os expoentes

$\dfrac{x^{a}}{x^{b}}=x^{a-b}$

Notação científica: A mantissa (o "coeficiente") deve ser maior ou igual a um e menor que 10:

$x*10^{n},~~1\le x<10$
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d)

$(5*10^{3})*7*10^{2}=5*10^{3}*7*10^{2}\\(5*10^{3})*7*10^{2}=(5*7)*(10^{3}*10^{2})\\(5*10^{3})*7*10^{2}=35*10^{3+2}\\(5*10^{3})*7*10^{2}=35*10^{5}\\(5*10^{3})*7*10^{2}=(3,5*10)*10^{5}\\(5*10^{3})*7*10^{2}=3,5*10^{1+5}\\\\\boxed{\boxed{(5*10^{3})*7*10^{2}=3,5*10^{6}}}$

e)

$(12*10^{2})\div(4*10^{2})=\dfrac{12*10^{2}}{4*10^{2}}\\\\\\(12*10^{2})\div(4*10^{2})=\dfrac{12}{4}*\dfrac{10^{2}}{10^{2}}\\\\\\(12*10^{2})\div(4*10^{2})=3*1\\\\\\\boxed{\boxed{(12*10^{2})\div(4*10^{2})=3}}$

f)

$(3*10^{3})\div(6*10^{3})=\dfrac{3*10^{3}}{6*10^{3}}\\\\\\(3*10^{3})\div(6*10^{3})=\dfrac{3*1}{6*1}\\\\\\(3*10^{3})\div(6*10^{3})=\dfrac{3\div3}{6\div3}\\\\\\\boxed{\boxed{(3*10^{3})\div(6*10^{3})=\dfrac{1}{2}}}$