Answer: [tex]\frac{x^{11}y^6}{9}[/tex]
Step-by-step explanation:
Remember the following:
- The Product of powers property:
[tex]a^m*a^n=a^{m+n}[/tex]
- The Quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
- And the Negative exponent rule:
[tex]\frac{1}{a}=a^{-1}[/tex]
Therefore, having the expression [tex]\frac{(3x^2y^{-3})}{27(xy)^{-9}}[/tex], you can simplify it by applying the properties mentioned before.
Then, you get:
[tex]\frac{(3x^2y^{-3})}{27(xy)^{-9}}=\frac{(3x^2)x^9y^{9}}{27(y)^{3}}=\frac{3x^{11}y^6}{27}=\frac{x^{11}y^6}{9}[/tex]
