1. The first expression is $\frac{6^{14}}{6}$. 2. Using the property of exponents $\frac{a^m}{a^n} = a^{m-n}$, simplify: $$\frac{6^{14}}{6} = 6^{14-1} = 6^{13}$$ 3. Next, simplify the expression $\frac{12^{13}}{2^{13}}$. 4. Write 12 as $2 \times 6$ or break down into primes as $12 = 2^2 \times 3$, so: $$12^{13} = (2^2 \times 3)^{13} = 2^{26} \times 3^{13}$$ 5. Substitute into the fraction: $$\frac{12^{13}}{2^{13}} = \frac{2^{26} \times 3^{13}}{2^{13}} = 2^{26-13} \times 3^{13} = 2^{13} \times 3^{13}$$ 6. Recognize that $2^{13} \times 3^{13} = (2 \times 3)^{13} = 6^{13}$. 7. Thus, $\frac{12^{13}}{2^{13}} = 6^{13}$. 8. Given expressions $6^{13}$ and $3^{13} \cdot 2^{13}$: 9. Since $3^{13} \cdot 2^{13} = (3 \times 2)^{13} = 6^{13}$, all expressions simplify or equal $6^{13}$. Final answer: All expressions equal $$6^{13}$$.