1.
$(x+1)^{12}$ -$(x+1)^{20}$ =0
=>$(x+1)^{12}$ =$(x+1)^{20}$
=>x+1=0=>x=-1
2.
$21^{7}$ .$49^{8}$ .$243^{5}$
=($3^{7}$ .$7^{7}$) .$7^{16}$ .$3^{25}$
=$3^{32}$ .$7^{25}$
3.
$\frac{35^{6}. 343^{2}. 125^{5}}{175^{12}}$
= $\frac{(7^{6} .5^{6}).7^{6} .5^{15}}{5^2.7}$
= $\frac{7^{12} .5^{21}}{5^2.7}$
=$5^{19}$ .$7^{11}$