The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. starting with 190 grams of a radioactive isotope, how much will be left after 6 half-lives?

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According to the definition of half-life, the mass of the radioactive isotope halfs its mass after each half-life, which means the remaining mass is always half the amount of the previous mass.  Therefore, after the 1st half-life, there is (190/2) g left; after the 2nd half-life, there is (190/2)/2 g left; so on and so forth.  After the 6th half-life, there is 190/(2*2*2*2*2*2) g = 190g/64 = 2.97 g left. So 2.97 g of this radioactive isotope will be left after 6 half-lives.

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