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 $\frac{1}{ {x}^{2} {y}^{2} }$