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.

The length of the subtangent to the curve x^m y^n = a^(m + n) at any point (x_1,y_1) on it is

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

Prove that by using the principle of mathematical induction for all n in N : 41^(n)-14^(n) is multiple of 27

Prove that by using the principle of mathematical induction for all n in N : 10^(2n-1)+1 is divisible by 11

Prove that by using the principle of mathematical induction for all n in N : 1.2.3+ 2.3.4+ ....+ n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

The length of the sub - tangent to the curve x^(m)y^(n) = a^(m+n) at any point (x_(1), y_(1)) on it is

Prove that by using the principle of mathematical induction for all n in N : 1+ 3+ 3^(2)+ …. + 3^(n-1)= ((3^(n)-1))/(2)

Prove that by using the principle of mathematical induction for all n in N : 1+2+3+.....+n lt (1)/(8)(2n+1)^(2)

Prove that by using the principle of mathematical induction for all n in N : x^(2n)-y^(2n) is divisible by x+y