Prove the rule of exponents `(ab)^n = a^n b^n` by using principle of mathematical induction for every natural number.

Show by using the principle of mathematical induction that for all natural number n gt 2, 2^(n) gt 2n+1

Prove each of the statements by the principle of mathematical induction : 2n lt (n + 2) ! for all natural number n .

Prove the statement by the principle of mathematical induction : 4^n - 1 is divisible by 3, for each natural number n .

Prove the following by using the principle of mathematical induction for all n in N 3^n gt 2^n

Prove each of the statements by the principle of mathematical induction : n^2 lt 2^n , for all natural numbers n gt= 5

Prove the statement by the principle of mathematical induction : For any natural numbers n, 7^n - 2^n is divisible by 5.

Prove the statement by the principle of mathematical induction : For any natural numbers n, x^n - y^n is divisible by x - y , where x and y any integers with x ne y

Prove the statement by the principle of mathematical induction : n^3 - 7n+ 3 is divisible by 3, for all natural number n .

Prove the statement by the principle of mathematical induction : 2^(3n) - 1 is divisible by 7, for all natural numbers n .

Prove the statement by the principle of mathematical induction : 3^(2n) - 1 is divisible by 8, for all natural number n.