What does "A1:A4^{1,2,3}" mean in an Excel formula?

Solution 1:

The caret signifies a power operation. The curly bracketed expression, {1,2,3}, is an array containing the values 1, 2, and 3.

As noted by @JasonClement, this formula only returns a value when entered as an array formula with Ctrl+Shift+Enter. As an array formula, the result is a 4-by-3 matrix containing the values below.

A1^1  A1^2  A1^3
A2^1  A2^2  A2^3
A3^1  A3^2  A3^3
A4^1  A4^2  A4^3

When entered in a single cell, however, only the top-left value of the matrix is returned.

The secret to this formula is that it must be entered as a single formula into a range the same size as the matrix. To do this, select an empty 4-by-3 range, e.g. D1:F4. Without changing the selection, click in the formula bar and type the formula. Then press Ctrl+Shift+Enter. You'll see the full matrix of results printed in the range you selected.

Solution 2:

The caret operator is for specifying an exponent. For instance, 2^4 will return 2 to the 4th power (2*2*2*2), which is 16.

Curly brackets like this are a way of defining an array, which could be used wherever a range could also be specified. For instance, using the INDEX formula with an array like so: =INDEX({2,5,7,9}, 4) will return the 4th item in the array: 9.

I have no idea what this formula is attempting to do. As it is, it results in an error. You can enter it as an array formula by pressing CTRL and SHIFT while pressing ENTER, but that will only return the value of the first cell (A1) raised to the first value in the given array (1), which is the same as 1.5 to the 1st power, which is 1.5.