Answer:
[tex]\huge\boxed{\sf \frac{160rs^5}{t^6}}[/tex]
Step-by-step explanation:
[tex]\sf 5r^6t^4 ( \frac{4r^3s^tt^4}{2r^4st^6} ) ^5[/tex]
Using rule of exponents [tex]\sf a^m/a^n = a^{m-n}[/tex]
[tex]\sf 5r^6t^4 ( 2 r^{3-4} s^{2-1}t^{4-6})^5\\5r^6t^4(2r^{-1}st^{-2})^5\\5r^6t^4 * 32 r^{-5}s^5t^{-10}[/tex]
Using rule of exponents [tex]\sf a^m*a^n = a^{m+n}[/tex]
[tex]\sf 160 r^{6-5}s^5t^{4-10}[/tex]
[tex]\sf 160 rs^5 t^{-6}[/tex]
To equalize the negative sign, we'll move t to the denominator
[tex]\sf \frac{160rs^5}{t^6}[/tex]
