Prove that $a^{n+m}=a^{n}a^m$, for real numbers
112080
Proving the Product Rule for exponents with the same base
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
25788
Prove that $i^i$ is a real number
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
89175
Proof of $(a+b)^{n+1}$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
142725
The general solution of $x^a = a^x$ for real $a >0$
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
127293
Prove that $(a-b) \mid (a^n-b^n)$
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog