Just Throw In Some Exponents

Number Theory Level 3

$\dfrac { { a }^{ 3 } }{ { b }^{ 2 } } =\dfrac { 3 }{ 16 }$ If all the $n$ pairs of positive integers $(a,b)$ that satisfy the equation above, where $a<100$ , are

$(a_1 ,b_1) , (a_2, b_2) , \ldots , (a_n, b_n) ,$

submit your answer as $\displaystyle \sum_{i=1}^n \dfrac{b_i}{a_i}$ .