Step 1: Identify the ether.
The compound \((CH_3)_3C-OC_2H_5\) is an ether with one tertiary group (tert-butyl) and one ethyl group.
Step 2: Rule for ether cleavage by HI.
When HI cleaves an ether, the iodide goes to the carbon that gives the more stable carbocation.
Step 3: Which carbocation is more stable?
The tert-butyl group forms a stable tertiary carbocation, so the C-O bond on that side breaks (SN1 path). The iodide attaches to the tert-butyl group.
Step 4: Decide the products.
So we get \((CH_3)_3C-I\), and the ethyl side leaves as \(C_2H_5-OH\) (ethanol).
Step 5: Conclusion.
The products are tert-butyl iodide and ethanol.
\[ \boxed{(CH_3)_3C\!-\!I \ \text{and}\ C_2H_5\!-\!OH} \]