How to show that the income elasticity of Marshallian demand is equal to unity? Suppose that the expenditure function is multiplicatively separable in $\textbf{p}$ and u so that 
$$e(p,u) =k(u)g(\textbf{p}),$$
 where k(·) is some positive monotonic function of a single variable, and g: $\mathbb{R^n_{+}}$ $\rightarrow$ $\mathbb{R}_{+}$.

Thank you in advance.
Here's my attempt at a hint, though I appreciate feedback, as I am not sure how rigorous this is. As per the comment I gave with the resource, your question seems to require a previous question in order to do this.

So start by showing that the share of income spent on good $x_i$ can always be measured by the elasticity of expenditure function with respect to $p_i$ at $(p, u^*)$ where $u^* = v(p,w)$

$$\mid \eta^ {e_{x_i, p_i}}\mid \ = \frac{\frac{\Delta x_i}{x_i}}{\frac{\Delta p_i}{p_i}} = \frac{\Delta x_i}{\Delta p_i} \cdot \frac{p_i}{x_i} = \frac{\partial x_i}{\partial p_i} \cdot \frac{p_i}{x_i}$$

We know that,

$$e(p,u^*) = p \cdot \tilde x, \forall \ \tilde x ∈ x^h (p, u^*) = x(p, e(p, u^*))$$

by duality, where $x^h(p, u^*)$ denotes Hicksian demand. So,

$$\frac{\partial e(p_i,u^*)}{\partial p_i} = x_i$$
$$\frac{\partial x_i}{\partial e(p_i, u^*)} = \frac{x_i}{w}$$

$$\implies \frac{\partial x_i}{\partial p_i} \cdot \frac{p_i}{x_i} = \frac{\partial e}{\partial p_i} \cdot \frac{\partial x_i}{\partial e}\cdot \frac{p_i}{x_i} = \frac {x_i^2}{w} \cdot \frac{p_i}{x_i} = \frac{p_i x_i}{w}$$

Which is the share of income spent on good $x_i$