Exponent problem

[Idontmath]

I ran into an issue today and it's kind of blowing my mind right now. I was under the assumption that -1^4=+1 but I ran into the problem 9-3^3-1^4. I thought that -1^4 in this problem would always be +1 but it's not. What am I not getting? Can someone please explain in the best detail possible why this problem is happening? And how do I know when -1^4 will equal 1 and when it will be -1.

Thanks for your time.

 

[Ishuda]

I ran into an issue today and it's kind of blowing my mind right now. I was under the assumption that -1^4=+1 but I ran into the problem 9-3^3-1^4. I thought that -1^4 in this problem would always be +1 but it's not. What am I not getting? Can someone please explain in the best detail possible why this problem is happening? And how do I know when -1^4 will equal 1 and when it will be -1.

Thanks for your time.

That is just one of the reasons one needs to be careful with grouping symbols:
-1^4 = - 1*1*1*1 = -1
(-1)^4 = (-1)*(-1)*(-1)*(-1) = 1
Sometimes you get lucky and both answers are the same
-3^3 = - 3*3*3 = -27
(-3)^3 = (-3)*(-3)*(-3) = -27
But that is only sometimes.