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

Simplify the following using the formula a^m xx a^n = a^(m+n) : p^5 xx p^8 .

Simplify the following using the formula a^m xx a^n = a^(m+n) : 3^11 xx 3^9 .

Use the identity (1+x)^(m)(1+x)^(n)=(1+x)^(m+n) to prove Vandermonde's theorem, ""^(m)C_(r ) +""^(m)C_(r-1). ""^(n)C_( 1)+""^(m)C_(r -2) *""^(n)C_(2) +….+""^(n)C_(r )=""^((m+n))C_(r )

Find: (6m+7n) (6m-7n)

Prove that triangleAOB~=triangleCOD by using SAS congruency rule.

If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)

IF the point P(x,y) be equidistant from the point A=(m+n,n-m), B=(m-n,m+n) then nx=………….

If tan alpha - tan beta =m and cot alpha - cot beta =n , then prove that cot ( alpha - beta )= (1)/(m)- (1)/(n)