Cardinal Arithmetic $a^ba^c = a^{b+c}$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
150320
Why does $a^{b}·a^{c}=a^{b+c}$?
20346
'Algebraic' way to prove the boolean identity $a + \overline{a}*b = a + b$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
48211
When is $(a+b)^n \equiv a^n+b^n$?
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
101708
Integers can be expressed as $a^3+b^3+c^3-3abc$
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
360
Modular exponentiation by hand ($a^b\bmod c$)
58267
Godel's pairing function and proving c = c*c for aleph cardinals
16553
Cardinality of the set of all total orders on $\Bbb{N}$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
90670
Prove $a^ab^bc^c\ge (abc)^{\frac{a+b+c}3}$ for positive numbers.
117047
exponentiation of cardinal number
87304
Solving for $x$ : $a^x+b^x=c$