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why is negative 5 in parenthesis to the 2nd power positive 25, and when it doesn't have parenthesis it equals negative 25

 Sep 8, 2017
 #1
avatar+7599 
+3

To see why...you need to know these things:

 

a2  =  a * a

 

A negative number times a negative number equals a positive number, e.g.       -3 * -4  =  12

 

Exponents come before multiplication in the order of operations, e.g.     6 * 32  =  6 * 9  =  54

 

And...     -4  =  -1 * 4

 

Try writing out the multiplication for your question. Can you figure it out now?  smiley

 Sep 8, 2017
 #2
avatar+100803 
+2

Thanks hectictar, i'd just like to add a little more.

 

\((-4)^2=-4*-4 =+16\)

Maybe that one is fairly obvvious to you..

If not then look better at Hectictar explanation.    smiley

 

 \(\text{So why is }-4^2\;\;\text{different ?}\\\)

 

Welll... Lets say that -42 did equal +16 (which is doesn't) and see what happens

\(30-4^2=30-16=14 \)

But 

\(30-4^2\;\;also\;\;=-4^2+30\)

If -42 = +16 then this answer becomes 16+30 = 46   which is obviously wrong because I know the answer is 14  !!

 

so the best way to think of it is this

\(-4^2=-1*4^2=-1*16=-16\) 

 

I hope that, together with Hectictar's answer, helps :)

 Sep 8, 2017

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