GRE Sample Test 3 Quantitative Reasoning 1

First, get rid of the negative exponents by expressing each base as its reciprocal:
$\frac{\frac{1}{{\mathit{x}}^{31}}}{{\mathit{y}}^2}$ = $\frac{1}{72}$ → $\left({\mathit{x}}^3\right)\left({\mathit{y}}^2\right)$ = 72
Next, break 72 down into its prime factors: 72 = 3 × 3 × 2 × 2 × 2. x = 2 and y = 3. x + y =5.