exam Maths Puzzle Numerical Ability

I am working on a Proof by Induction and keep getting bogged down in the exponents in the inductive step. Please help me simplify:

5/2[2/3(2^n - 2^(-n))] - 2/3(2^(n-1)- 2^(n-1))

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exam Other Question

The perimeter of a rectangle is to be no greater than 300 in.,
and the length must be 125 in.
Find the maximum width of the rectangle. Prove that ((AC)^2/(BC)^2)=(AD/BD) In right triangle ACB (C is the right angle) with CD as an altitude (D is between A and B)