# Simple question yet oh so hard for me. TT__TT

1. ### .hacker//Kazu

26
Evaluate and express as a fraction in lowest terms

-3 to the power of 4 + (-3)to the power of 3 - (-3)to the power of 2.

(I apoligize...I don't know how to type powers on the computer...>_<)

I tried to evaluate it like it told me to...so I ended up with

81-27+9
=63

Yet when I checked the answers sheet, it said the anwer was -117.

What I want to know is WHY? Am I doing something wrong? TT_____TT

2. ### sutupidmath

$$-3^{4}+(-3)^{3}-(-3)^{2}$$ i think this is what you meant, because your notation is a little ambiguous. then if this is the case we have
$$-3^{4}+(-3)^{3}-(-3)^{2}=-81-27-9=-117$$ well there are two mistakes on what you did, first $$-3^{4}=-81$$ and not 81, pay heed, the minus sign is not included whithin the power, so the power does not actually affect the sign here, also $$-(-3)^{2}=-9$$ be carefull again the first minus sign is not included within the power, so the power of two only affects(changes) the second minus sign that is included whithin the bracktets. I hope this helps!

3. ### .hacker//Kazu

26
I see. Thank you so much. I was always confused by why there were brackets sometimes. So if there are no brackets around the integer, the power does not affect it and it stays the same, but if there is a bracket, the power affects it, even power being positive, odd being negative. I think I understand.

Thank you very much. ^_____________^

4. ### sutupidmath

here are a couple of examples i will write down for you

$$-2^{4}=-16$$ wheras $$(-2)^{4}=16$$
$$(-3)^{2}=9$$
$$(-3)^{3}=-27$$ you see that odd powers do not affect the sign even if the sign is included within the brackets.
$$-(-4)^{2}=-16$$ wheras $$-(-4)^{3}=64$$