Question

Can someone please help!! (Simplifying exponential equations)

Answer 1

Seems we undistributed the $( \frac{5}{2} )^x$

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