$(a_{1}+4)(a_{2}+4)(a_{3}+4)(a_{4}+4)(a_{5}+4).$

If $a_{1}, a_{2}, a_{3}, a_{4}$ and $a_{5}$ are the fifth roots of 1088, then find the value of the expression above.

The answer is 2112.

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Note that $a_1$ , $a_2$ , $a_3$ , $a_4$ , $a_5$ are the roots of the equation $x^5 - 1088 = 0.$ Hence, the $(a_i + 4)$ 's are the roots of the equation $(x-4)^5 - 1088 = 0, \\ x^5 + \dots - 2112 = 0.$ Since the product of the roots of the equation above is given by $- (-2112)/1 = 2112$ , the desired product is $\boxed{2112}$ .