Question

Simplify (x^-1y^2)(-3x^2y^0)


Please help and explain

Answer 1

We have
`x^(-n) = \frac1{x^n}` if
`n` is a positive integer and
`x\\eq0`, as well as
`x^0 = 1` if
`x\\eq0`. So right away we can simplify to

`\left(x^(-1) y^2\right) \left(-3 x^2 y^0\right) = \left(\frac{y^2}x\right) \left(-3x^2\right) = -\frac{3x^2y^2}x`

If
`x=0`, then the starting expression is undefined. So we accept that
`x=0`, in which case
`\frac xx = 1`, and the overall expression simplifies to

`\left(x^(-1) y^2\right) \left(-3 x^2 y^0\right) = \boxed{-3xy^2}`