Question 1174244
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You start with


    {{{2r^3}}} = -16


Divide both sides by 2


    {{{r^3}}} = -16/2 = -8


Take cube root from both sides


    r = {{{root(3,-8)}}} = -2.


<U>ANSWER</U>.   The solution is r= -2.   It is a unique solution to this equation over real domain.
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Solved.