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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?

 Aug 22, 2014

Best Answer 

 #1
avatar+3450 
+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 -42

In your head your thinking -(42) = -(4 x 4) = -(16) = -16

 

Does this help you out at all?

 Aug 22, 2014
 #1
avatar+3450 
+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 -42

In your head your thinking -(42) = -(4 x 4) = -(16) = -16

 

Does this help you out at all?

NinjaDevo Aug 22, 2014
 #2
avatar+98044 
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......

 

 

 Aug 22, 2014
 #3
avatar+3450 
+5

Sure thing, I'll add that.

 Aug 22, 2014
 #4
avatar+99122 
+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    $$(-4)^2=16$$

 

  $$But what about $27-4^2$ ? \\
No-one would want to interpret this as $27+(-4)^2 = 27+16=43$ That would be really odd.\\
Of course not $27-4^2=27-16=11$\\\\
so here it is really obvious that -4^2=-1*4^2=-1*16=-16$$
 

 Aug 22, 2014

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