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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

Guest Sep 8, 2017

#1**+3 **

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

a^{2} = 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 * 3^{2} = 6 * 9 = 54

And... -4 = -1 * 4

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

hectictar Sep 8, 2017

#2**+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.

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

Welll... Lets say that -4^{2} 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 -4^{2} = +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 :)

Melody Sep 8, 2017