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# PPPLLLLSSSS HELP!!!!

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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
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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? Sep 8, 2017
#2
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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. $$\text{So why is }-4^2\;\;\text{different ?}\\$$

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