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I know this probably is a silly stupid question, but I just don't get it. I'm currently doing Khan Academy pre-algebra and stumbled upon an awkward problem. I assume that:

$-5-8^{2}=59$

Because -8 squared is 64 and et cetera. But the right answer is actually -69. I sincerely don't get why. I told my wife, she's sure it should be 59 too. Can someone explain to me how comes it is -69?

wswld
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    $-5-8^2=-5-64$ while $-5+(-8)^2=-5+64$... – anderstood Oct 30 '15 at 21:18
  • You probably thought something like "$-5-8^2 = -5+(-8^2)$. Now $-8^2 = -1 * 8^2$, which is equal to $-64$, and not $64$, since order of operations means you square the $8$ first before multiplying by $-1$. – Joey Zou Oct 30 '15 at 21:22

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The correct order of the operations is: first calculate the powers than add the results. So in you case: $$-5-8^2=-5-(8^2)=-5-64=-69$$

Emilio Novati
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It's just convention in the priority of the operations. Exponents are done before any addition/substraction If we add brackets, your expression becomes:

$$ ( -5 )- ( 8^2 ) $$

Thus it is $-69$.

Why was that chose? Simple, as you said in you answer, there is no difference between $(-8)^2$ and $8^2$ so $(-5) + ((-8)^2)$ could just have been written $(-5) + (8^2)$. Not as interesting as the other priority order.

Lærne
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