Can any Power function (whose base is not zero) , e.g. $2^{n}$, be defined arithmetically (i.e. using addition and multiplication only)?
59679
How is exponentiation defined in Peano arithmetic?
1948
How do you raise a Java BigInteger to the power of a BigInteger without doing modular arithmetic?
131708
Sum of powers of natural numbers
48211
When is $(a+b)^n \equiv a^n+b^n$?
97984
Express as sum of powers
33877
What does $2^x$ really mean when $x$ is not an integer?
34666
Prove that the expression cannot be a power of 2
38636
A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
118314
How to define $x^a$ for arbitrary real numbers $x$ and $a$
134348
When is $(p - 1)! + 1$ a power of $p$?
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
50110
How to check if a number is a power of 2
74664
A question regarding power series expansion of an entire function
108497
Can $2^n$ and $2^{n+1}$ have the same digit sum?
51402
Is multiplication not just repeated addition?
61673
Could I define 0^0 to be 1?
64896
Dealing with non-integral powers on negative numbers