In the statements below $n>0,$a and $b$ are integer constants. Prove the following statements using the definitions of the complexity

notation.

$($i$)2^{an}in(2^n),a1.$

$($ii$)2^{n+a}$inO$(2^n),a0.$

$($iii$)lo{g}_{a}n+2^{n+b}in(2^n),a,b2.$