Answer:
[tex]\frac{1}{x^2y^{2}}[/tex]
A is the correct option.
Step-by-step explanation:
The given expression is [tex]\frac{x^0y^{-3}}{x^2y^{-1}}[/tex]
We know that any number raised with zero power equals 1. Thus, [tex]x^0=1[/tex]
Hence, the expression becomes
[tex]\frac{y^{-3}}{x^2y^{-1}}[/tex]
Now, apply the quotient rule, [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this rule, we have
[tex]\frac{1}{x^2y^{-1-(-3)}}[/tex]
[tex]=\frac{1}{x^2y^{-1+3}}[/tex]
[tex]=\frac{1}{x^2y^{2}}[/tex]
Hence, the simplified expression is [tex]\frac{1}{x^2y^{2}}[/tex]
A is the correct option.
