a)
\frac{(6^2)^6*6}{6^{12}}=\frac{6^{12}*6}{6^{12}}=6
b)
\frac{5^6*5*5^0}{5^4}=\frac{5^{6+1+0}}{5^4}=\frac{5^7}{5^4}=5^{7-4}=5^3=125
c)
\frac{(a^5)^4*a^0*a^{20}}{a^{16}:a^3}=\frac{a^{20+0+20}}{a^{16-3}}=\frac{a^{40}}{a^{13}}=a^{40-13}=a^{27}
d)
\frac{(x^0)^6*(x^{16})^0}{((x^{16})^2:x^{16})^0}=\frac{x^0*x^0}{(x^{32-16})^0}=\frac{x^0}{(x^{16})^0}=\frac{x^0}{x^0}=x^0=1
a^0=1
e)
\frac{5^{13}:(5^6*5^2)}{5^3}=\frac{5^{13}:5^8}{5^3}=\frac{5^5}{5^3}=5^2=25