seems we undistributed the [tex]( \frac{5}{2} )^x[/tex]
remember
[tex]x^{a+b}=(x^a)(x^b)[/tex]
factor out [tex]( \frac{5}{2} )^x[/tex] from each term on the left side
[tex]1( \frac{5}{2} )^x+( \frac{5}{2} )^3( \frac{5}{2} )^x=A( \frac{5}{2} )^x[/tex]
undistribute [tex]( \frac{5}{2} )^x[/tex]
[tex]( \frac{5}{2} )^x(1+( \frac{5}{2} )^3)=A( \frac{5}{2} )^x[/tex]
divide both sides by [tex]( \frac{5}{2} )^x[/tex]
[tex] 1+( \frac{5}{2} )^3=A [/tex]
