Data structures and algorithms

Question

Is 2^(n+1) = O(2^n)?

&

Is 2^(2n) = O(2^n)?

Answer 1

1) 2ⁿ⁺¹ = O(2ⁿ)

because

2ⁿ⁺¹ = 2×2ⁿ, which is a constant multiple of 2ⁿ.

2) 2²ⁿ ≠ O(2ⁿ)

because

2²ⁿ = 2ⁿ×2ⁿ, which is not a constant multiple of 2ⁿ.