Answer: 8
Work Shown:
[tex]\frac{2^x \times 3^y}{2^4 \times 3^2} = 6\\\\\frac{2^x \times 3^y}{2^4 \times 3^2} = 2\times3\\\\\frac{2^x \times 3^y}{2^4 \times 3^2} = 2^1\times3^1\\\\2^x \times 3^y = (2^4 \times 3^2)(2^1\times 3^1)\\\\2^x \times 3^y = (2^4\times2^1) (3^2\times 3^1)\\\\2^x \times 3^y = 2^{4+1} \times 3^{2+1}\\\\2^x \times 3^y = 2^{5} \times 3^{3}\\\\[/tex]
The 2^x matches with 2^5, showing that x = 5.
3^y matches with 3^3 to get y = 3
Therefore, x+y = 5+3 = 8
