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Algebraic attacks have received a lot of attention in studying security of symmetric ciphers. The function used in a symmetric cipher should have high algebraic immunity (${\cal AI}$) to resist algebraic attacks. In this paper we are interested in finding ${\cal AI}$ of Boolean power functions. We give an upper bound on the ${\cal AI}$ of any Boolean power function and a formula to find its corresponding low degree multiples. We prove that the upper bound on the ${\cal AI}$ for Boolean power functions with Inverse, Kasami and Niho exponents are $\lfloor \sqrt{n}\rfloor + \lceil \frac{n}{\lfloor \sqrt{n} \rfloor}\rceil -2$, $\lfloor \sqrt{n} \rfloor + \lceil \frac{n}{\lfloor \sqrt{n} \rfloor}\rceil$ and $\lfloor \sqrt{n} \rfloor + \lceil \frac{n}{\lfloor \sqrt{n} \rfloor}\rceil$ respectively. We also generalize this idea to Boolean polynomial functions. All existing algorithms to determine ${\cal AI}$ and corresponding low degree multiples become too complex if the function has more than 25 variables. In our approach no algorithm is required. The ${\cal AI}$ and low degree multiples can be obtained directly from the given formula.