# 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 \( \displaystyle \sum_{i=1}^n \dfrac{b_i}{a_i} \).