simple math question

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maybe my brain isn't working right this morning but I was grading my dd's math test this morning and she got this question wrong. I got the same answer as she did.

What is negative 6 squared? There are no parenthesis involved. I would think that a negative times a negative would equal a positive so the answer would be positive 36. The book says that the answer is negative 36.

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maybe my brain isn't working right this morning but I was grading my dd's math test this morning and she got this question wrong. I got the same answer as she did.

What is negative 6 squared? There are no parenthesis involved. I would think that a negative times a negative would equal a positive so the answer would be positive 36. The book says that the answer is negative 36.

Without parentheses to indicate otherwise, the answer is positive 36.

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Thank you. I can't believe the textbook is wrong.

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If written as -6^2, the answer is -36. The exponent is applied to the 6, not the negative.

If written as (-6)^2, the answer is 36. Here, the exponent is applied to the negative and the 6.

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The answer to (-6) squared is 36, but the answer to -6 squared is -36. In the first you are squaring -6, but in the second you are taking the negative of 6 squared. I hope this makes sense.

Linda

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Thank you. I can't believe the textbook is wrong.

The textbook is NOT wrong. In the order of operations the exponent comes before the negative. Therefore, without parentheses, -6 squared is -36. You square the 6 first to get 36, then apply the negative sign.

Parentheses come before exponents, so if one wants to square (-6) one has to use parentheses to do it properly and get +36.

Edited to add... ok, I'm the slowest typer!

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One way to "see" it as well is think about if the problem were 100 - 6^2.

You wouldn't write the next step as 100 + 36, you'd write 100 -36.

So if the 100 isn't there, then -6^2 = -36.

Recognizing what's the base with exponents is really important.

(-6)^2 the base is -6. We have (-6)(-6) = 36

-6^2, the base is 6 and we have the opposite of it. So - 6*6 = -36.

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ok, now I'm confused. It seems that everyone is getting a different answer. I thought that without parenthesis it would be negative six times negative six, which equals positive 36.

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ok, now I'm confused. It seems that everyone is getting a different answer. I thought that without parenthesis it would be negative six times negative six, which equals positive 36.

It's -36.

Also, from purplemath

Exponents and Negative Numbers (page 4 of 4) Sections: Introduction, Adding and subtracting, Multiplying and dividing, Negatives and exponents

Now you can move on to exponents, using the cancelation-of-minus-signs property of multiplication. For instance, (3)^2 = (3)(3) = 9. In the same way:

• Simplify (â€“3)^2

• (â€“3)^2 = (â€“3)(â€“3) = (+3)(+3) = 9

Note the difference between the above exercise and the following:

• Simplify â€“3^2

• â€“3^2 = â€“(3)(3) = (â€“1)(9) = â€“9

In the second exercise, the square (the "to the power 2") was only on the 3; it was not on the minus sign. Those parentheses make all the difference in the world! Be careful with them, especially when you are entering expressions into software. Different software may treat the same expression very differently, as one researcher has demonstrated very thoroughly.

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