A rule that we need to know in order to solve this is:
[tex](a^b)^c=a^{bc}[/tex]The extended rule would be:
[tex](\frac{a^b}{c^d})^x=\frac{a^{bx}}{c^{dx}}[/tex]Also, remember another rule:
[tex]\frac{1}{a^{-x}}=a^x[/tex]Keeping all these rules in mind, we can simplify:
[tex](\frac{4^3}{5^{-2}})^5=\frac{4^{15}}{5^{-10}}=4^{15}\cdot5^{10}[/tex]THis is the final form.