IS BASIC EXPONENTIATION BROKEN ?

[prime stag]

When an equation is solved in 2 different ways , In one way the result is "inconsistent" and bu another way we can find a "real solution"

[quiet juniper]

1 = (-1)^2 = 1^2 but when we take both sides to the power of 1/2, -1 = 1
is math broken??

no
(a^b)^c is not always a^(bc)

even though we like to ignore this fact whenever possible

for real exponentiation it works whenever c is not an odd multiple of 1/2, 1/4, 1/6, etc

*citation needed