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

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

2 Answers

5 votes

Answer:

you cnat

Explanation:

User Bmdhacks
by
8.5k points
1 vote

Answer:

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

User Gabriel Theodoulos
by
7.9k points

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