Sorting The Exponentials

When the set $$\left( 3^{100},2^{140},3^{90} \right)$$ is sorted, we get $$\left( 2^{140},3^{90},3^{100} \right)$$.

Sort this set of 100 exponentials and find the sum of the exponents of the elements with even indices.

Details and assumptions.

• An index is the position of an item in a list. For example in the list $$\left(a,b,c,d\right)$$, the index of $$a$$ is $$0$$, $$b$$ is $$1$$, $$c$$ is $$2$$ and the index of $$d$$ is $$3$$. The sum of all the elements with even indices is $$a+c$$.
×