Question

Simplificar a expressão (0,001)^3. [(0,001)^2]^-3 / (0,01) . (0,0001)^4

Answer 1

$\ \ \ \frac{(0,001)^3\cdot [(0,001)^2]^{-3}}{ (0,01)}\cdot (0,0001)^4= \frac{(10^{-3})^3\cdot [(10^{-3})^2]^{-3}}{10^{-2}}\cdot (10^{-4})^4\\ \\= \frac{10^{-9}\ \cdot \ 10^{18}}{10^{-2}}\cdot 10^{-16}=10^{-9+18-(-2)}\cdot10^{-16}=10^{-9+18+2}\cdot10^{-16}\\ \\=10^{11}\cdot10^{-16}=10^{11+(-16)}=10^{11-16}=10^{-5}$

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$\ \ \ \frac{(0,001)^3\cdot [(0,001)^2]^{-3}}{ (0,01) \cdot (0,0001)^4}= \frac{(10^{-3})^3\cdot [(10^{-3})^2]^{-3}}{ 10^{-2} \cdot (10^{-4})^4}\\ \\= \frac{10^{-9}\cdot 10^{18}}{10^{-2} \cdot 10^{-16}}= \frac{10^{-9+18}}{10^{-2+(-16)}}= \frac{10^3}{10^{-2-16}}= \frac{10^9}{10^{-18}}= 10^{9-(-18)}=10^{9+18}\\ \\=10^{27}$