I will give you a brainliest if correct

Part A;
(6)^2x = 6^0, after opening the brackets and any number power zero equals to one.
then,
aⁿ = a^b , in exponential form
n = b
then
2x = 0
x = 0.
Part B,
since any number power zero equals to 1.
6^0 = 1
then,
1^x = 1^1
from, aⁿ = a^b
n = b
then,
x = 1.
or,
1 = 6^0
then,
(6^0)^x = 6^0
6^0x = 6^0
equating,
0x = 0
x = 0.