mathematics - Find $n^{23}$ with the least multiplication

$n$ is an arbitrary real number. By only using multiplication, you are asked to find $n^{23}$ with the least amount of multiplication operation.

Note: You can only use $n$ or the results you can with multiplications as examplified below.

For example if this question is asked for $n^4$, the answer would be $2$:

1.

$n\times n=n^2$

2.

$n^2\times n^2=n^4$

Answer

1.

$n \times n = n^2$

2.

$n\times n^2 = n^3$

3.

$n^3\times n^2=n^5$

4.

$n^5\times n^5=n^{10}$

5.

$n^{10}\times n^{10}=n^{20}$

6.

$n^{20}\times n^{3}=n^{23}$