Question

What is the multiplicative inverse of `- \frac{z^3}{2xy^2}`?

Answer 1

The muplticative inverse of a number `x` is, by definition, a number `y` such that `x\cdot y=1`.

So, in case of integer numbers `n`, the multiplicative inverse of `n` is simply `\frac{1}{n}`, and thus it's not an integer number.

In the case of fractions, instead, the multiplicative inverse of a fraction is still a fraction, and it's simply a fraction with the same positivity of the original one, and with numerator and denominator flipped over: the multiplicative inverse of `\frac{a}{b}` is the fraction `\frac{b}{a}`. So, in your case, the multiplicative inverse of `-\frac{z^3}{2xy^2}` is `-\frac{2xy^2}{z^3}`.