Why does -3^2*(-3)^2 = -81

Louvre 0
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Why does -3^2*(-3)^2 = -81 ? Whereas both -3^2 and (-3)^2 both equals 9. I've run the equation in wolfram alpha and it does indeed give the results stated above.

wolfram-mathematica math
2 Answers

See https://en.wikipedia.org/wiki/Order_of_operations

The order of operations, which is used throughout mathematics, science, technology and many computer programming languages, is expressed here:

  1. exponentiation and root extraction
  2. multiplication and division
  3. addition and subtraction

So 1 + 2 × 3 = 7

and 0 - 3^2 = -9

See specifically https://en.wikipedia.org/wiki/Order_of_operations#Unary_minus_sign

There are differing conventions concerning the unary operator − (usually read "minus"). In written or printed mathematics, the expression −3^2 is interpreted to mean −(3^2) = −9.

In some applications and programming languages, notably Microsoft Excel, PlanMaker (and other spreadsheet applications) and the programming language bc, unary operators have a higher priority than binary operators, that is, the unary minus has higher precedence than exponentiation, so in those languages −3^2 will be interpreted as (−3)^2 = 9.

Chris Degnen0

From the link from a comment from FheFungusAmongsUs

−x^2, in every mathematical context I have seen, always means −(x^2). So −3^2=−9.

Link

Louvre0
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