Simplify 4 to the 13 power divided by 3 to the -5 power

To simplify the expression 4^13 ÷ 3^-5, we can use the rule a^m ÷ a^n = a^(m-n).

Therefore, 4^13 ÷ 3^-5 = 4^(13-(-5)) = 4^13 x 3^5 = 4^13 x 3^5

The expression is already simplified, so the final answer is 4^13 x 3^5.