Question

Simplify x^0 y^-3/x^2y^-1

Answer 1

The answer is 1/x^2y^2

Answer 2

The given expression is
`\frac{ {x}^(0) y { - }^(3) }{ {x}^(2)y { - }^(1) }`

We know that any number raised with zero power equals 1. Thus,
`{x}^(0) = 1`

Hence, the expression becomes

`\frac{y { - }^(3) }{ {x}^(2) y { - }^(1) }`

Now, apply the quotient rule,
`\frac{ {x}^( \alpha ) }{ {x}^(b) } = {x}^( \alpha - b)`

Using this rule, we have

`\frac{1}{ {x}^(2) y { - }^(1 - ( - 3)) }`

`= \frac{1}{ {x}^(2) y { - }^(1 + 3) }`

`= \frac{1}{ {x}^(2) {y}^(2) }`

Hence, the simplified expression is
`\frac{1}{ {x}^(2) {y}^(2) }`