a)
2^4*3^4=6^4=36^2 -------------------6^4=(6^2)^2=36^2
4^5*9^5=36^5=6^{10} -------------------36^5=(6^2)^5=6^{10}
(3^3)^4=3^{12}
(5^2)^6=5^12=125^4 ------------------- 5^{12}=(5^3)^4=125^4
b)
2^9*2^{-1}=2^8=4^4-------------------2^8=(2^2)^4
3^{-5}*3^3=3^{-2}=(\frac{1}{9})^1 -------------------3^{-2}=(\frac{1}{3})^2=\frac{1}{9}
6^{-3}:6^7=6^4=36^2 -------------------6^4=(6^2)^2=36^2
10^8:5^8=2^8=16^2 -------------------2^8=(2^4)^2=16^2