When two numbers with like signs are multiplied (positive times a positive, or negative times negative) the result will always be positive.
If the two numbers do not have the same sign, and are multiplied, it will always result with a negative number (positive times negative, and vice versa).
1.) negative times negative = positive
2.) negative squared is the same as negative times negative, = positive
3.) (-1) (-12)^3 can be thought of as
(-1) (-12) (-12) (-12), starting from left to right when multiplied will result with
(-1 * -12) negative times negative, result positive,
(12 * -12) previous positive result times negative, results negative
(-144 * -12) previous negative result times negative, results positive
4.) Same as above, if we start the operation from left to right
negative times negative, results positive
previous positive result times positive, result positive
previous positive result times negative, results negative