Given that 27^1/4 / 3^x = 9^2/7 work out the exact value of x.

I think this is  :

27^(1/4) / 3^x = 9^(2/7)

(3^3)^(1/4) / 3^x  = (3^2)^(2/7)

3^(3/4) / 3^x  = 3^(4/7)    rearrange as

[ 3^(3/4) ] / [ 3^(4/7) ] =  3^x    

[ 3^ ( 3/4 - 4/7) ]  = 3^x

[ 3 ^ [ (21 - 16) / 28 ]  = 3^x

3^(5/28)  = 3^x

So  x  =  5/28