goldsjo wrote:

this is an actual practice problem i came across

if x = -1, what is -x^2?

is it 1 or -1?

The interpretation of -x^2 as -(x^2) is correct according to agreements made by international math authorities. It is more convincing when it is typeset properly with the exponent as a superset number. Another way of getting this right is to substitute "(-1)*" for the "-".

Hence -x^2 = (-1)*x^2 and it is clearly (-1)*(x^2).

What makes this a somewhat confusing question is that: 1) most of the popular lists of algebraic precedence rules (e.g., PEMDAS) ignore the unary functions "+" and "-" when it should be properly placed below Exponentiation and above Multiplication/Division; and 2) one of the most widely used programs, Microsoft Excel, treats -x^y as (-x)^y on the spreadsheet. Try it! (The 600 pound gorilla acknowledges the "error" but has no intention of fixing it and possibly breaking millions of existing spreadsheets). Interestingly enough, the macro language built in Excel, VBA, treats -x^y properly as -(x^y).

just in case you were wondering....

_________________

Best,

AkamaiBrah

Former Senior Instructor, Manhattan GMAT and VeritasPrep

Vice President, Midtown NYC Investment Bank, Structured Finance IT

MFE, Haas School of Business, UC Berkeley, Class of 2005

MBA, Anderson School of Management, UCLA, Class of 1993