Simplify 11^(2a) ÷ 11^5: Exponential Division Problem

To solve this problem, we apply the Power of a Quotient Rule for Exponents, which states that for any non-zero base $a$ and integers $m$ and $n$, the expression $\frac{a^m}{a^n} = a^{m-n}$. In this case, our base $a$ is 11.

Given the expression $\frac{11^{2a}}{11^5}$, let's simplify it using the rule:

• The numerator is $11^{2a}$.
• The denominator is $11^5$.

Applying the rule:

$\frac{11^{2a}}{11^5} = 11^{2a-5}$

Thus, the expression simplifies to $11^{2a-5}$.

So, the solution to the question is: $11^{2a-5}$