The rules of exponents tell you that you can distribute the exponent to each of the factors. When one already has an exponent, those exponents multiply.
[tex](-5p^{4}z^{6}u)^{3}=(-5)^{3}\cdot(p^{4})^{3}\cdot(z^{6})^{3}\cdot u^{3}\\\\=-125p^{4\cdot 3}z^{6\cdot 3}u^{3}\\\\=-125p^{12}z^{18}u^{3}[/tex]
