Exponent rules with negative numbers

Question

Hello if you could answer this please what is the difference between -2^2 and (-2)^2

Answer 1

$$-2^2=(-1)2^2=-4$$ and $$(-2)^2=(-1)^2(2)^2=(-1)(-1)(4)=4$$

Answer 2

It is assumed that

$$-2^2=-(2^2)=-4\;,\;\;\text{whereas}\;\;(-2)^2=4$$

Answer 3

Just an extra here, Derrick. Please do NOT resort to the scientific calculator. The TI30 will show -2 to the power 2 as 4 without brackets, whereas Ti84 for example will show -4. I deal with this issue in class every semester. Calculators mean it well, but their order of operations is not always the "same" as what we have in our minds. Learn the rules of exponents without the calculator. It's better.

Answer 4

In view of the other answers here: the difference between -2^2 and (-2)^2 is 8. :-)