The given expression is:

$\frac{5^{12}}{5^2 \times 5}$

Let's simplify this step by step.

Step 1: Combine the powers in the denominator.

Since $5^2 \times 5$ is equivalent to $5^2 \times 5^1$, you can add the exponents in the denominator: $5^2 \times 5 = 5^{2+1} = 5^3$

Step 2: Simplify the fraction.

Now the expression becomes: $\frac{5^{12}}{5^3}$

Using the rule of exponents $\frac{a^m}{a^n} = a^{m-n}$, we subtract the exponents: $5^{12 - 3} = 5^9$

Thus, the simplified expression is:

$5^9$

This is the final answer.

Do you want further details or have any questions?

Here are some related questions for practice:

1. How would you simplify $\frac{2^8}{2^3 \times 2}$?
2. What is $\frac{7^{10}}{7^2 \times 7^3}$?
3. How do you express $\frac{x^{15}}{x^5}$ in simplified form?
4. Simplify $\frac{a^{7}}{a^3 \times a^2}$.
5. What is the value of $\frac{10^{9}}{10^3}$?

Tip: When simplifying exponents, remember that dividing powers with the same base means subtracting their exponents.