Quick Arithmetic Question

[maya.perl]

"If x and y are negative odd integers, is the following always, sometimes or never positive: 4x + 3y - y ^ -x + x^3 ?"

I would say sometimes, given that the expression -y^-x (no parenthesis of any sort in the original question) varies with the values of x and y--the expression results in a negative number to a negative power, and is preceded by a minus sine.. so it should be positive! The answer states never, arguing that -y^-x is actually -1/(y^x)... but if x is negative and the minus sines cancel out, wouldn't that bring the exponent back up?

I'm confused and definitely thought I had basic arithmetic down.... your help is much much appreciated! Thanks!

[tommywallach]

Hey Maya,

You're forgetting that y and x are ODD. y itself will be negative, and it will be raised to a positive power (because x is negative, so -x will be positive). But any negative number raised to an ODD integer is STILL negative. So that term will remain negative, like the other three in the expression (4x, 3y, and x^3). Make sense?

-t