$a)\dfrac{3^9.3^{20}.2^8}{3^{24}.243.2^6}$
$=\dfrac{3^{9+20}.2^8}{3^{24}.3^5.2^6}$
$=\dfrac{3^{29}.2^8}{3^{24+5}.2^6}$
$=\dfrac{3^{29}.2^8}{3^{29}.2^6}$
$=\dfrac{2^8}{2^6}$
$=2^8:2^6$
$=2^{8-6}$
$=2^2$
$=4$
$b)$`(215.5^3. 2^6 .3^4)/(8.2^18 .81.5)`
`=(5.43.5^3 .2^6 .3^4)/(8.2^18 .3^4 .5)`
`=(43.5^{1+2}.2^6)/(8.2^{6+6}.5 )`
`=(43.5^2)/(8.2^6)`
`=(43.25)/(8.64)`
`=1075/512`