Answer:
see explanation
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] , [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
[tex]2^{(n+1)}[/tex] + [tex]2^{(n-1)}[/tex]
= [tex]2^{n}[/tex] × [tex]2^{1}[/tex] + [tex]2^{n}[/tex] × [tex]2^{-1}[/tex] ← factor out [tex]2^{n}[/tex] from each term
= [tex]2^{n}[/tex] ( 2 + [tex]\frac{1}{2}[/tex] )
= [tex]\frac{5}{2}[/tex] × [tex]2^{n}[/tex]
= 5 × [tex]2^{-1}[/tex] × [tex]2^{n}[/tex]
= 5([tex]2^{(n-1)}[/tex] ) ← in factored form
