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!

- Thread starter marlousie
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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!

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- Jun 18, 2007

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- 22,781

-4^2= 1/16................................................... i

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

However:

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

Please come back if you have more questions.

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You are wrong about THATI 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 \(4^{-2}=\frac{1}{16}\)

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- May 3, 2019

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- 355

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.

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!

Ah, thank you I realize my mistake now! Thank you, I appreciate it-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.

Thank you for the correct way I understand where I went wrong now!You are wrong about THAT

\(-4^2=-16\) while \(4^{-2}=\frac{1}{16}\)

Thank you for this! I understand I was wrong in my original post but this explained another problem that I probably would've come across the way!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.