a) (7^x)^9 = 7^81
7^(9x) = 7^81
9x = 81
x = 9
b) (8^5)^40 = 2^(30x)
8^200 = 2^(30x)
(2^3)^200 = 2^(30x)
2^600 = 2^(30x)
600 = 30x
x = 600:30
x = 20
c) 10^13 = 50^13 : x^13
10^13 = (50:x)^13
10 = 50:x
x = 50:10
x = 5
d) (20:x)^30 = 4^30
20:x = 4
x = 20:4
x = 5