(c)(a^(m))^(n)=a^(mn)

Third law If a is a non-zero rational number and mn are integers then (a^(m))^(n)=a^(mn)=(a^(n))^(m)

Second law If a is a non-zero rational number and mn are integers then a^(m)-:a^(n)=a^(m-n) or (a^(m))/(a^(n))=a^(m-n)

We know that (a^m)^n = a^(mn) Let a^m = x , then m = log_ax x^n = a^(mn) , then log_ax^n= mn = n log_ax (why?)

The number of ways in which we can distribute mn students equally among m sections is given by a.((mn!))/(n!) b.((mn)!)/((n!)^(m))c((mn)!)/(m!n!)d.(mn)^(m)

If a,m,n are positive integers,then {anm}^(mn) is equal to a^(mn)( b) a(c)a^((m)/(n))(d)1

If the ratio of the roots of the quadratic equation ax^(2)+bx+c=0 be m:n, then prove that ((m+n)^2)/(mn)=(b^(2))/(ac)

If ratio of the roots of the equation ax^(2)+bx+c=0 is m:n then (A) (m)/(n)+(n)/(m)=(b^(2))/(ac) (B) sqrt((m)/(n))+sqrt((n)/(m))=(b)/(sqrt(ac))],[" (C) sqrt((m)/(n))+sqrt((n)/(m))=(b^(2))/(ac)]

If x,y is positive real numbers then maximum value of (x^(m)y^(m))/((1+x^(2m))(1+y^(2n))) is (A)(1)/(4)(B)(1)/(2) (C) (m+n)/(6mn) (D) 1

If a^m a^n =a^(mn) , then express m in terms of n.

If x,y is positive real numbers then maximum value of (x^my^n)/((1+x^(2m))(1+y^(2n))) is (A) 1/4 (B) 1/2 (C) (m+n)/(6mn) (D) 1