Question

simplifique?

$\frac{0,1 \times 0,001}{10.000 \times 100} =$


$\frac{10 \times (0,1) {}^{2} }{0,00001 \times 1000} =$
​

Answer 1

$a)\\\\\frac{0,1\times0,001}{10000\times100}~=~\frac{\frac{1}{10}\times\frac{1}{1000}}{10^4\times10^2}~=~\frac{10^{-1}\times\frac{1}{10^3}}{10^4\times10^2}~=~\frac{10^{-1}\times10^{-3}}{10^4\times10^2}~=\\\\\\=~10^{-1+(-3)-(4)-(2)}~=~\boxed{10^{-10}}$

$b)\\\\\frac{10\times(0,1)^2}{0,00001\times1000}~=~\frac{10^1\times(\frac{1}{10})^2}{\frac{1}{100000}\times1000}~=~\frac{10^1\times\frac{1}{10^2}}{\frac{1}{10^5}\times10^3}~=~\frac{10^1\times10^{-2}}{10^{-5}\times10^3}~=\\\\\\=~10^{\,1+(-2)-(-5)-(3)}~=~10^{1}~=~\boxed{10}$