For what values of n will (2^n)^n < (2^n)(2^n)? Please give examples of those values in your explanations.

Question

help me answer this question please!!

Answer 1

(2^n)^n=2^n^2; 2^n * 2^n=2^2n; so 2^n^2<2^2n and n^2<2n.

n^2-2n<0; n(n-2)<0, so (a) n<0 and n>2 OR (b) n>0 and n<2, because the signs have to be different to make the product negative.

(a) can't be satisfied but (b) can: 0<n<2, n is between 0 and 2.

CHECK

Put n=1: 2<4 TRUE.

Put n=0: 1<1 NOT TRUE, which satisfies the conditions of inequality.

Put n=2: 16<16 NOT TRUE, which satisfies the conditions of inequality.

Put n=√2: 2^(1/4)<2 or 2<16 TRUE.