Problem Solving

Official Guide 12th edition. Page 175. Q 164.

If m^-1 = -1/3, then m^-2 is equal to:

I got -1/9 because we do not know whether the - sign is from the numerator or the denominator, and the m^-2 would square the denominator, however the book says 1/9. So I am confused. Are they just assuming that the negative sign is from the denominator?

Thank you!

Hi bfman,

I wouldn't have worried about the sign of numerator or the denominator, because when you square the fraction you will square both the numerator and the denominator. So whichever is -ve, on squaring the term you will get a +ve result. Thus
m^-2 = (m^-1)^2 = (-1/3)^2 = 1/9

Hope this helps,
Vivek.