To simplify the expression $\frac{x^5}{x^{-7}}$, you can use the property of exponents that states:

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

Here, $a = x$, $m = 5$, and $n = -7$. Applying the property, we get:

$\frac{x^5}{x^{-7}} = x^{5 - (-7)}$

$x^{5 + 7} = x^{12}$

Therefore, the simplified form of $\frac{x^5}{x^{-7}}$ is:

$x^{12}$

Would you like more details or have any questions? Here are some related questions you might consider:

1. How would you simplify $\frac{x^8}{x^2}$?
2. What is the result of $\frac{y^{-3}}{y^{-5}}$?
3. How do you simplify $x^0$?
4. If $\frac{x^a}{x^b} = x^{c}$, what is the relationship between $a$, $b$, and