Question

How to factorize 2^{n+1}+2^{n-1}?

I know the answer is 5(2^{n-1}), but how do i get there?

Answer 1

you cnat

Explanation:

Answer 2

see explanation

Explanation:

Using the rules of exponents

`a^(m)` ×
`a^(n)` ⇔
`a^((m+n))` ,
`a^(-m)` =
`(1)/(a^(m) )`

`2^((n+1))` +
`2^((n-1))`

=
`2^(n)` ×
`2^(1)` +
`2^(n)` ×
`2^(-1)` ← factor out
`2^(n)` from each term

=
`2^(n)` ( 2 +
`(1)/(2)` )

=
`(5)/(2)` ×
`2^(n)`

= 5 ×
`2^(-1)` ×
`2^(n)`

= 5(
`2^((n-1))` ) ← in factored form