Can you help me, i'm confused about exponents

i just read that 4^-2 is the same as 1/4^2. but i noticed that 4^2 - 4^4 = -12, which does not = 1/4^2. How can this be? I thought that 4^2 - 4^4 = 4^-2

No ,

the true statement is : 4^2 / 4^4 = 4^-2

when they're divided , the exponents are subtracted

Yes, 4^(-2) is the same as 1/4^2.
but 4^2 - 4^4 does not equal 4^-2.

(4^2) / (4^4) = 4^(-2)

when you divide, the exponents subtract.

when you multiply, the exponents add together.

4^2 - 4^4 does not equal -12. because 4^2 = 16 and 4^4 = 256

so 16 - 256 = -240

4^2 / 4^4 = 4^(-2) = 1/4^2

the problem asks for subtraction, not division

4^-2 is 0.0625
4^2 is 16.
4^4 is 265.
16 - 265 = -249
-124.5^2 is -249.
o.o'

4^2 - 4^4 = 16 - 256 = - 240