The given expression is:

$\frac{6^5}{6^3}$

To simplify this, apply the quotient rule for exponents:

$\frac{a^m}{a^n} = a^{m-n}$

Here, $a = 6$, $m = 5$, and $n = 3$. So,

$\frac{6^5}{6^3} = 6^{5-3} = 6^2$

Thus, the simplified expression is:

$6^2 = 36$

Would you like more details or have any questions?

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Here are five related questions to consider:

1. How would you simplify $\frac{6^7}{6^2}$?
2. Can you apply the same rule to simplify $\frac{5^6}{5^4}$?
3. How do you simplify $\frac{a^8}{a^3}$ for any base $a$?
4. What happens if the exponents are negative, like $\frac{6^5}{6^{-2}}$?
5. How do you simplify $\frac{6^5}{6^5}$?

Tip: When dividing powers with the same base, always subtract the exponents!