Find the geometric mean of the following set of numbers: 4, 8, 16, 32.

Step 1 ：Step 1: Understand that the geometric mean of a set of numbers is the nth root of the product of the numbers, where n is the count of numbers. The formula for the geometric mean (\(\bar{G}\)) of n numbers (\(x_1, x_2, ..., x_n\)) is \(\bar{G} = \sqrt[n]{x_1 \cdot x_2 \cdot ... \cdot x_n}\)

Step 2 ：Step 2: Substitute the given values into the formula. So \(\bar{G} = \sqrt[4]{4 \cdot 8 \cdot 16 \cdot 32}\)

Step 3 ：Step 3: Simplify the equation to find the geometric mean. So \(\bar{G} = \sqrt[4]{32768} = 8\)