If a and b are positive natural numbers `a^(1/n) xx b^(1/n) = (ab)^(1/n`

Let a and b be two positive unequal numbers , then (a^(n+1)+b^(n+1))/(a^(n)+b^(n)) represents

If a>b and n is a positive integer,then prove that a^(n)-b^(n)>n(ab)^((n-1)/2)(a-b)

If a,b and n are natural numbers then a^(2n-1)+b^(2n-1) is divisible by

Statement-1: If a, b are positive real numbers such that a^(3)+b^(3)=16 , then a+ble4. Statement-2: If a, b are positive real numbers and ngt1 , then (a^(n)+b^(n))/(2)ge((a+b)/(2))^(n)

If a and b are non-zero rational numbers and n is a natural number then (a^(n))/(b^(n))=((a)/(b))^(n)

For natural number n , 2^n (n-1)!lt n^n , if