a. \(\left(a^5\right)^7=a^{5.7}=a^{35}\)
b. \(\left(a^6\right)^4:a^{12}=a^{6.4}:a^{12}=a^{24}:a^{12}=a^{24-12}=a^{12}\)
c.\(\left(2^3\right)^5:\left(2^3\right)^3=2^{3.5}:2^{3.3}=2^{15}:2^9=2^{15-9}=2^6=64\)
d. \(\left(3^2\right)^4:\left(3^3\right)^2=3^{2.4}:3^{3.2}=3^8:3^6=3^{8-6}=3^2=9\)