Rules of math

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Probability

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Somebody posted this...

- 6^2 - 6^0 = ?

My understanding...

- 6^2 = - 36... But - 6^0 = - 1

so...

- 36 - 1 = - 37... But some guy comes along and says you should use parentheses, which were not used in the original math problem?

so...

(- 6)^2 (- 6)^0 = 36

Who's correct?
 
Probability said:
Somebody posted this...

- 6^2 - 6^0 = ?

My understanding...

- 6^2 = - 36... But - 6^0 = - 1

so...

- 36 - 1 = - 37... But some guy comes along and says you should use parentheses, which were not used in the original math problem?

so...

(- 6)^2 (- 6)^0 = 36

Who's correct?
Click to expand...
You are correct, of course. What rule is there that says you should insert those parentheses??

The rule that does apply is that exponents are done before multiplication, which includes the implied multiplication by -1. So

[math]-6^2-6^0=-(6^2)-(6^0)=-36-1=-37[/math]
What he did assumed wrongly that [imath]-6^2=(-6)^2[/imath], and also, very foolishly, changed a subtraction into a multiplication:

[math]-6^2{\color{Red}-}6^0\ne(-6)^2{\color{Red}\cdot}(-6)^0[/math]
So you can ignore him, among many others. You can add parentheses for clarity, as I did here, but only when they don't change the meaning.
 
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