Question

if (81)^x=1/(125)^y,then find the value of 12xy

Answer 1

$( 81) {}^{x} = ( \frac{1}{125} ) {}^{y} \\ (3) {}^{4x} = ( \frac{1}{5}) {}^{3y} \\ or \: (3) {}^{4x} \times (5) {}^{3y} = 1 \\ or \: (3) {}^{4x} \times (5) {}^{3y} = (3) {}^{0} \times (5) {}^{0}$
When bases are same we equate powers.
So, 4x=0&3y=0
So, x=0&y=0
So, 12xy=12*0*0=0