If a negative number is in parenthesis and has a positive exponent, how does it get a positive number outcome while a negative number without a parenthesis and an exponent gets a negative outcome?
+3453 Consider the example (-3)2
This is really saying (-3) x (-3) = (-(-9)) = (9)
This only works for even exponets though. I'll show you with the example (-2)3
This is really saying (-2) x (-2) x (-2) = (-(-4)) x (-2) = (-(-(-8))) = (-8)
If you don't have parentheses, your basically imagining that there are parentheses after the negative sign. So, say you had -42
In your head your thinking -(42) = -(4 x 4) = -(16) = -16
Does this help you out at all?
+3453 Consider the example (-3)2
This is really saying (-3) x (-3) = (-(-9)) = (9)
This only works for even exponets though. I'll show you with the example (-2)3
This is really saying (-2) x (-2) x (-2) = (-(-4)) x (-2) = (-(-(-8))) = (-8)
If you don't have parentheses, your basically imagining that there are parentheses after the negative sign. So, say you had -42
In your head your thinking -(42) = -(4 x 4) = -(16) = -16
Does this help you out at all?
+128475 Thanks for that detailed explanation, ND.........this is something that gives a lot of students trouble!!!!
Maybe you should add this to "Great AnswersTo Learn From".......just a suggestion......
+118609 Yes a great explanation Ninja, I'd like to add just a little.
people do not like the fact that $$-4^2=16$$
the surface it appears that it should be thought of as $$(-4)^2=16$$
$$But what about $27-4^2$ ? \\
No-one would want to interpret this as $27+(-4)^2 = 27+16=43$ That would be really odd.\\
Of course not $27-4^2=27-16=11$\\\\
so here it is really obvious that -4^2=-1*4^2=-1*16=-16$$
