Sharpe Ratio Annualized

In the CFAI reading 3.1 of Portfolio Management, Analysis of Active Retrun. the book takes a monthly return and make it to an annual return by multiplying by 12. I would have thought they would have raised it to the power of 12 to account for compounding. Any insight into why the did this, and if that was a mistake?

The expected value over a number of observations equals the expected value of a single observation * the number of observations.

In other words: If you flip 2 coins, the expected number of heads is 1. If you flip 6 coins, the expected number of heads is 3.