The initial velocity for the reaction will be #"350 nmol s"^(-1)#.
Start from the Michaelis-Menten equation
#V_0 = (V_"max" * [S])/(V_"max" + [S])#
When an uncompetitive inhibitor is introduced, the equation takes this form
#V_0 = (V_"max" * [S])/(K_m + [S] * underbrace((1 + ([I])/K_I))_(alpha)#
But #(1 + ([I])/K_I)# is actually equal to #alpha#, the degree of inhibition, which implies that the equation becomes
#V_0 = (V_"max" * [S])/(K_m + [S] * alpha)#
Now plug your values and solve for #V_0#
#V_0 = ("950 nmol s"^(-1) * 350cancel(mu"mol L"^(-1)))/((175+ 350 * 2.20)cancel(mu"mol L"^(-1))#
#V_0 = 350/(945) * "950 nmol s"^(-1) = "351.85 nmol s"^(-1)#
Rounded to two sig figs, the number of sig figs given for #V_"max"# and #[S]#, the answer will be
#V_0 = color(green)("350 nmol s"^(-1))#
