# Just need a little clearing up

#### marlousie

##### New member
I tried to ask google however it didn't really give me a straight answer so I made an account here solely for this question. It's also relatively simple so thank you to anyone who explains it to me because I'm still a bit caught up on it.

Why does (-4)^2= 16 but -4^2= 1/16

I'm currently studying for the SAT and these things constantly trip me up because my math teachers never really went over this.

Thank you again!

#### Subhotosh Khan

##### Super Moderator
Staff member
I tried to ask google however it didn't really give me a straight answer so I made an account here solely for this question. It's also relatively simple so thank you to anyone who explains it to me because I'm still a bit caught up on it.

Why does (-4)^2= 16 but -4^2= 1/16

I'm currently studying for the SAT and these things constantly trip me up because my math teachers never really went over this.

Thank you again!
-4^2= 1/16................................................... is incorrect

-4^2 = - (4^2) = -(16) = -16

However:

4^(-2) = 1/(4^2) = 1/16

Please come back if you have more questions.

#### pka

##### Elite Member
I tried to ask google however it didn't really give me a straight answer so I made an account here solely for this question. It's also relatively simple so thank you to anyone who explains it to me because I'm still a bit caught up on it.
Why does (-4)^2= 16 but -4^2= 1/16
I'm currently studying for the SAT and these things constantly trip me up because my math teachers never really went over this.
$$-4^2=-16$$ while $$4^{-2}=\frac{1}{16}$$

#### LCKurtz

##### Full Member
I tried to ask google however it didn't really give me a straight answer so I made an account here solely for this question. It's also relatively simple so thank you to anyone who explains it to me because I'm still a bit caught up on it.

Why does (-4)^2= 16 but -4^2= 1/16

I'm currently studying for the SAT and these things constantly trip me up because my math teachers never really went over this.

Thank you again!
It has to do with the precedence of operators. Exponentiation takes precedence over addition and multiplication. So if have $$\displaystyle -4^2$$, you would to the exponent first giving $$\displaystyle -16$$. Such problems are avoided by using parentheses. $$\displaystyle (-4)^2 = 16$$ versus $$\displaystyle -(4^2)=-16$$. Then there is no doubt which is meant. On exams like the SAT they give you $$\displaystyle -4^2$$ to trip you up if you don't know the precedence rules.

#### marlousie

##### New member
-4^2= 1/16................................................... is incorrect

-4^2 = - (4^2) = -(16) = -16

However:

4^(-2) = 1/(4^2) = 1/16

Please come back if you have more questions.
Ah, thank you I realize my mistake now! Thank you, I appreciate it

#### marlousie

##### New member
$$-4^2=-16$$ while $$4^{-2}=\frac{1}{16}$$
It has to do with the precedence of operators. Exponentiation takes precedence over addition and multiplication. So if have $$\displaystyle -4^2$$, you would to the exponent first giving $$\displaystyle -16$$. Such problems are avoided by using parentheses. $$\displaystyle (-4)^2 = 16$$ versus $$\displaystyle -(4^2)=-16$$. Then there is no doubt which is meant. On exams like the SAT they give you $$\displaystyle -4^2$$ to trip you up if you don't know the precedence rules.