Prove the quotient rule using `a^m/a^n=a^(m-n)`

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

Prove the following by using iduction for all n in N . 1+2+3+.....+n=(n(n+1))/(2)

In the expansion of (1+a)^m+n , prove that coefficients of a^m and a^n are equal.

If m and n are the two natural number such that m^(n)=25 , then find the value of n^(m) :-

If m and n are the two natural number such that m^(n)=9 , then find the value of n^(m) :-

Prove the following by using the principle of mathematical induction for all n in N n(n+1)(n+5) is a multiple of 3

Prove the following by using the principle of mathematical induction for all n in N 41^n - 14^n is a multiple of 27.

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

Prove the following by using the principle of mathematical induction for all n in N (2n+7) lt (n+3)^2

Prove the following by using the principle of mathematical induction for all n in N 7^n - 3^n is divisible by 4.