Show that: `((a+1/b)^m xx\ (a-1/b)^n)/((b+1/a)^m\ xx\ (b-1/a)^n)=(a/b)^(m+n)`

Show that: (a+(1)/(b))^(m)x(a-(1)/(b))^(n)(b+(1)/(a))^(m)x(b-(1)/(a))^(n)=((a)/(b))^(m+n)

Show that : ((a^(m))/(a^(-n)))^(m-n)xx((a^(n))/(a^(-1)))^(n-1)xx((a^(l))/(a^(-m)))^(l-m)=1

a^m xx b^n=3087 then a+b=

Find n so that: (i) (a^(n+1)+b^(n+1))/(a^(n)+b^(n)) (ii) (a^(n)+b^(n))/(a^(n-1)+b^(n-10) may be A.M. between a and b.

Solve the followings : (a^(m-n))^(1) xx (a^(n-1))^m xx (a^(1 - m))^(n)

Simplify: (i)\ ((x^(a+b))/(x^c))^(a-b)\ ((x^(b+c))/(x^a))^(b-c)\ ((x^(c+a))/(x^b))^(c-a) (ii)\ ((x^l)/(x^m))^(1/(lm))\ xx\ ((x^m)/(x^n))^(1/(mn))\ xx\ \ ((x^n)/(x^l))^(1/(ln))

The cofficient of x^(n) in (x)/((x-a)(x-b)) is (a^(n)-b^(n))/(a-b)xx(1)/(a^(n)b^(n))