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?
+3454 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?
+3454 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?
+130477 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......
+118703 Yes a great explanation Ninja, I'd like to add just a little.
people do not like the fact that −42=16
the surface it appears that it should be thought of as (−4)2=16
Butwhatabout$27−42$?No−onewouldwanttointerpretthisas$27+(−4)2=27+16=43$Thatwouldbereallyodd.Ofcoursenot$27−42=27−16=11$sohereitisreallyobviousthat−42=−1∗42=−1∗16=−16
