$a)a^{3}.a^{5}=a^{3+5}=a^{8}$
$b)x^{7}.x.x^{4}=x^{7+1+4}=x^{12}$
$c)3^{5}.4^{5}=(3.4)^{5}=12^{5}$
$d)8^{5}.2^{3}=(2^{3})^{5}.2^{3}=2^{15}.2^{3}=2^{15+3}=2^{18}$
$e)5^{6}:5^{3}=5^{6-3}=5^{3}$
$f)3^{15}:3^{5}=3^{15-5}=3^{10}$
$g)a^{4}:a=a^{4-1}=a^{3}$
$h)4^{6}:4^{6}=1$
$i)9^{8}:3^{2}=9^{8}:9=9^{8-1}=9^{7}$
$k)3.3^{4}.3^{5}=3^{1+4+5}=3^{10}$
$l)7^{3}:7^{2}:7=7^{3-2-1}=7^{0}$
$m)(x^{4})^{3}=x^{4.3}=x^{12}$
$n)4^{8}.8^{4}$
$=4^{8}.2^{4}.4^{4}$
$=4^{8+4}.2^{4}$
$=4^{12}.(2^{2})^{2}$
$=4^{12}.4^{2}$
$=4^{12+2}$
$=4^{14}$
$o)5^{12}.7-5^{11}.10$
$=5^{11}.5.7-5^{11}.10$
$=5^{11}(35-10)$
$=5^{11}.25$
$=5^{11}.5^{2}$
$=5^{11+2}=5^{13}$
$p)2^{20}.15+2^{10}.85$
$=2^{10}.15(2^{10}+70)$
$q)27^{16}:9^{10}$
$=(3^{3})^{16}:(3^{2})^{10}$
$=3^{48}:3^{20}$
$=3^{48-20}$
$=3^{28}$
$r)125^{3}:25^{4}$
$=(5^{3})^{3}:(5^{2})^{4}$
$=5^{9}:5^{8}$
$=5^{1}=5$
$s)24^{4}:3^{4}-32^{12}:16^{12}$
$=(24:3)^{4}-(32:16)^{12}$
$=8^{4}-2^{12}$
$=(2^{3})^{4}-2^{12}$
$=2^12-2^{12}$
$=0$
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