$a)\frac{6^8\cdot 5^8}{{15}^8}=\frac{{\left(6\cdot 5\right)}^8}{{15}^8}=\frac{{30}^8}{{15}^8}={\left(\frac{30}{15}\right)}^8=2^8=4^4={16}^2=256$

$b)\frac{7^4\cdot 3^4\cdot 5^4}{{21}^4}=\frac{{\left(7\cdot 3\cdot 5\right)}^4}{{21}^4}=\frac{{\left(21\cdot 5\right)}^4}{{21}^4}={\left(\frac{21\cdot 5}{21}\right)}^4=5^4={25}^2=625$