Function: $f(x)=\frac{2}{3}(7)^{3 x}-5$
Select one or more:
Vertical Stretch
Vertical Compression
Vertical Reflection (over $x$-axis)
Vertical Shift Up
Vertical Shift Down
Horizontal Stretch
Horizontal Compression
Horizontal Reflection (over $y$-axis)
Horizontal Shift Right
Horizontal Shift Left

Step 1 ：The function $f(x)=\frac{2}{3}(7)^{3 x}-5$ is an exponential function with base $a=7$.

Step 2 ：The function is modified by multiplying the output by $\frac{2}{3}$, which is a vertical compression because it makes the graph narrower along the $y$-axis.

Step 3 ：The function is also modified by subtracting $5$, which is a vertical shift down because it moves the entire graph down by $5$ units.

Step 4 ：Lastly, the function is modified by multiplying the input $x$ by $3$, which is a horizontal compression because it makes the graph narrower along the $x$-axis.

Step 5 ：\(\boxed{\text{The transformations applied to the base function are: Vertical Compression, Vertical Shift Down, and Horizontal Compression.}}\)