Step 1: Understanding the NMR peaks.
The \( ^1 \)H NMR spectrum of 1,3,5-tri-isopropylbenzene shows distinct multiplet peaks due to the protons on the benzene ring and the isopropyl groups. Each set of equivalent protons will produce its own set of peaks. For this molecule, the proton environment is quite symmetric, and the chemical shifts will form multiplets.
Step 2: Counting the multiplets.
In the case of 1,3,5-tri-isopropylbenzene, we have 7 distinct proton environments that will each produce a separate multiplet.
Step 3: Conclusion.
The total number of multiplet peaks in the \( ^1 \)H NMR spectrum of 1,3,5-tri-isopropylbenzene is 7.