Question

If m = a^x ,n = a^y then m^y n^x​

Answer 1

Answer:

$m^y n^x$ $=a^{2xy}$

Step-by-step explanation:

$m = a^x$ . . . . . . . . . . . . . . . .   (i)

$n = a^y$ . . . . . . . . . . . . . . . .   (ii)

$m^y n^x$

$=(a^x)^y (a^y)^x$  [putting values of m and n from equation (i) and (ii) respectively]

$=a^{xy} a^{yx}$  [∵ $(a^m)^n = a^{mn}$]

$=a^{xy} a^{xy}$

$=a^{(xy + xy)}$  [∵ $a^m.a^n = a^{(m+n)}$]

$=a^{2xy}$