Is gross domestic product equal to the sum of personal consumption expenditures, gross exports, and government expenditures?
This statement of the components of Gross Domestic Product is not complete. It is missing one major component. All of the components listed here are parts of GDP when GDP is measured using the expenditure approach. However, the expenditure approach also takes into account what is called "gross private domestic investment." This component of GDP is the amount that businesses spend to buy assets that they expect to use to make money in the future. The equation that is generally used is GDP = C (personal consumption) + I (investment) + G (government expenditures) + (X-M). "X-M" stands for exports minus imports, which is the definition of gross exports.
So, the statement you have given is an incomplete description of the expenditures method of measuring GDP.