Answer:
The simplified form of the expression is [tex]\frac{1}{x^{7} y^{4}}[/tex].
Step-by-step explanation:
The expression is:
[tex]\frac{x^{-3}\cdot y^{2}}{x^{4}\cdot y^{6}}[/tex]
The division rule of exponents is:
[tex]a^{m}\div a^{n}=a^{m-n}[/tex]
The negative exponent rule is:
[tex]a^{-m}=\frac{1}{a^{m}}[/tex]
Simplify the expression as follows:
[tex]\frac{x^{-3}\cdot y^{2}}{x^{4}\cdot y^{6}}=[x^{-3-4}]\times [y^{2-6}][/tex]
[tex]=x^{-7}\times y^{-4}\\\\=\frac{1}{x^{7} y^{4}}[/tex]
Thus, the simplified form of the expression is [tex]\frac{1}{x^{7} y^{4}}[/tex].
