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First,remove the square root with a square. That is

2^{x - 1 }= 2

3^{y}^{- 2 }= 3^{2}

The next step is to linearize the equation by multiplying through with log.

The equation becomes:

log(2)^{x - 1 }= log(2)

(x - 1)log(2) = log(2)

Dividing through by log(2)

(x - 1) = 1

x = 2

log(3)^{y}^{- 2 }= log(3)^{2}

(y - 2)log(3) = 2log(3)

Dividing through by log(3)

y - 2 = 2

y = 2

Therefore, y/x = 4/2 = 2

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