Question

Sabendo que x=10^2 e y=10^-1, calcule o valor da expressão.

Answer 1

Primeiro vamos substituir o que a gente já sabe o valor:
$x = 10^{2} \\ \\ y = 10^{-1}$

$\frac{((10^{2})^{-1}.(10^{-1})^{2})^{-1}.((10^{2})^{2}.(10^{-1})^{-1})^{2}.((10^{2}).(10^{-1}))^{2}}{((10^{2})^{2}.(10^{-1})^{-1})^{-1}.((10^{2})^{-1}.(10^{-1})^{2})^{-2}}$

E, sabendo que $( x^{2} )^{3} = x^{2.3} = x^{6}$:

$\frac{(10^{-2}.10^{-2})^{-1}.(10^{4}.10^{1})^{2}.(10^{2}.10^{-1})^{2}}{(10^{4}.10^{1})^{-1}.(10^{-2}.10^{-2})^{-2}}$

Lembrando que $x^{10} . x^{10} = x^{10+10} = x^{20}$

$\frac{(10^{-4})^{-1}.(10^{5})^{2}.(10^{1})^{2}}{(10^{5})^{-1}.(10^{-4})^{-2}}$

$\frac{10^{4}.10^{10}.10^{2}}{10^{-5}.10^{8}} \\ \\ \frac{10^{16}}{10^{3}}$

E agora que $\frac{ x^{8} }{ x^{5} } = x^{8-5} = x^{3}$

$\frac{10^{16}}{10^{3}} = 10^{16-3} = 10^{13}$

Answer 2

Oloco bixo,tinha questao menos trabalhosa nao?
(10^4 . 10^10 . 10^2)/(10^-5 . 10^8)

10^16/10^3
10^13