1) $\frac{16^{3} . 125^{4}}{20^6 . 25^4}$
= $\frac{(2^4)^3 .(5^3)^4}{4^6 . 5^6 . (5^2)^4}$
= $\frac{2^{12} . 5^{12} }{2^{12}. 5^{14}}$
= $\frac{1}{5^2}$ = $\frac{1}{25}$
2) $\frac{2^{15} . 9^4 }{6^6 . 8^3}$
= $\frac{2^{15} . (3^2)^4}{2^6. 3^6 . (2^3)^3}$
= $\frac{2^{15} . 3^8}{2^{15} . 3^6}$
= $3^{2}$ = 9
3) $\frac{3^5 . 27^3}{81 . 9^4}$
= $\frac{3^5 . (3^3)^3}{3^4 . (3^2)^4}$
= $\frac{3^5 . 3^9}{3^4 . 3^8}$
= $\frac{3^{14}}{3^{12}} = $3^{2}$ = 9