Question 386514
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Hi, You are absolutely correct 
4^x (2^y)=16
(2^2x)(2^y) = 2^4
In general, {{{(x^m)(x^n) = x^(m+n)}}}
 2^(2x+y) = 2^4      both sides of equation with the same base
    {{{ 2x + y = 4 }}}  Exponents are also equal

8^x= 2^(y/2)
 2^3x = 2^(y/2)
   3x = y/2
   6x = y

   2x + y = 4
   2x + 6x = 4  Substituting  6x for y
       8x = 4  
        x = 1/2   y = 3   (6*(1/2)