[" sinypity - "],[qquad ((x')/(x^(m)))'ln(x^(m))/(x^(n)))^(y_(mn))*((x^(n))/(x^(2)))^(prime/nx)]

Prove root(ln)((x^(l))/(x^(n)))xxroot(nm)((x^(n))/(x^(m)))xxroot(ml)((x^(m))/(x^(l)))=1

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))

If f(x)=((x^l)/(x^m))^(l+m)((x^m)/(x^n))^(m+n)((x^n)/(x^l))^(n+l) , then f^(prime)(x) is equal to (a) 1 (b) 0 (c) x^(l+m+n) (d) none of these

If x^(m)y^(n)=(x+y)^(m+n)

Suppose n,m are natural numbers and f(x)=|(1,(1+x)^(m),(1+mx)^(mn)),((1+mx)^(n),1,(1+nx)^(mn)),((1+nx)^(m),(1+x)^(n),1)| constant term of the polynomial f(x) is

If x^(m)y^(n)=(x+y)^(m+n) , then (dy)/(dx)=

Simply (x^(m)/x^(n))^(m^(2)+mn+n^(2))xx(x^(n)/x^(l))^(n^(2)+nl+l^(2))xx(x^(l)/x^(m))^(l^(2)+lm+m^(2))

The HCF of (x^(3)y)/(m^(2)n^(4)), (x^(2)y^(3))/(m^(2)n^(2)) and (x^(4)y^(2))/(mn^(3)) is

Show that: (x)+(x+(1)/(n))+(x+(2)/(n))+...+(x+(n-1)/(n))=nx+(n-1)/(2)