Answer
$$pH = 13.592$$
Work Step by Step
$$1.55 \% \space NaOH : \frac{1.55 \space g \space NaOH}{100 \space g \space Solution}$$ Molar mass :
$Na: 22.99g $
$O: 16.00g $
$H: 1.008g$
22.99g + 16.00g + 1.008g = 40.00g
$$\frac{1.01 \space g \space Solution}{1 \space mL \space Solution} \times \frac{1.55 \space g \space NaOH}{100 \space g \space Solution} \times \frac{1 \space mole \space NaOH}{40.00 \space g \space NaOH} \times \frac{1000 \space mL}{1 \space L} = 0.391 \space M \space NaOH$$
$$[OH^-] = [NaOH] = 0.391 \space M$$ $$[H_3O^+] = \frac{K_w}{[OH^-]} = \frac{10^{-14}}{0.391} = 2.56 \times 10^{-14}$$ $$pH = -log(2.56 \times 10^{-14}) = 13.592$$
