To simplify the expression and rewrite it in the form $a^n$, we use the laws of exponents:

$a^m \cdot a^n = a^{m+n}$

For $a^5 \cdot a^{-3}$:

$a^{5} \cdot a^{-3} = a^{5 + (-3)} = a^{5 - 3} = a^2$

Thus, the simplified expression is:

$a^2$

Would you like further clarification on this process?

5 Related Questions:

1. How would this rule apply if the exponents were fractions, like $a^{3/4} \cdot a^{-1/2}$?
2. Can this same law be used for division, such as $a^5 / a^3$?
3. How does the zero exponent rule ($a^0 = 1$) fit with these laws?
4. What happens if the base $a$ is a negative number in this expression?
5. How does this apply to roots, such as $a^{5/2} \cdot a^{-3/2}$?

Tip:

Always ensure the base $a$ is the same before applying exponent rules!