Given the equation:
[tex]((5x-16)^3-4)^3=216000[/tex]Applying the exponent laws:
[tex]\begin{gathered} \sqrt[3]{((5x-16)^3-4)^3}=\sqrt[3]{216000} \\ (5x-16)^3-4=60 \end{gathered}[/tex]Simplify:
[tex]\begin{gathered} (5x-16)^3-4+4=60+4 \\ (5x-16)^3=64 \end{gathered}[/tex]Applying the exponent laws:
[tex]\begin{gathered} \sqrt[3]{(5x-16)^3}=\sqrt[3]{64} \\ Simplify \\ 5x-16=4 \\ 5x-16+16=4+16 \\ 5x=20 \\ \frac{5x}{5}=\frac{20}{5} \\ x=4 \end{gathered}[/tex]Answer: x = 4
