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?

Guest Aug 22, 2014

#1**+10 **

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 -4^{2}

In your head your thinking -(4^{2}) = -(4 x 4) = -(16) = **-16**

Does this help you out at all?

NinjaDevo
Aug 22, 2014

#1**+10 **

Best Answer

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 -4^{2}

In your head your thinking -(4^{2}) = -(4 x 4) = -(16) = **-16**

Does this help you out at all?

NinjaDevo
Aug 22, 2014

#2**0 **

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......

CPhill
Aug 22, 2014

#4**+5 **

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$$

Melody
Aug 22, 2014