Math CentralQuandaries & Queries


Question from Andrea, a teacher:

Is -4 squared the same as (-4) squared? I am thinking the first is -16 and the second is +16. I am trying to clarify for my students.


Hi Andrea,

I wouldn't mix arithmetic expressions like -4 with english words like squared. There are certain conventions in evaluating arithmetical expressions that remove the ambiguity caused by -4 squared.

In evaluating arithmetic expressions, exponentiation (powers) are performed before multiplication or addition. Thus for -42 you should evaluate 42 first to obtain 16 and then multiply by -1 to get

-42 = -16.

Parentheses in mathematical expressions are used as commas are sometimes used in english, to group objects together. Hence in (-4)2 the exponent is applied to the entire expression -4. Hence

(-4)2 = (-4) × (-4) = 16.

I hope this helps,

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