Answer:
1/(xy²)
Explanation:
The given expression is
[tex]\frac{x^{-4}y^{-2}z^7}{x^{-3}z^7}[/tex]
To simplify the expression, we will use the following properties
[tex]\begin{gathered} \frac{x^a}{x^b}=x^{a-b} \\ x^{-a}=\frac{1}{x^a} \end{gathered}[/tex]
So, we need to apply the first property for x and z to get:
[tex]\begin{gathered} \frac{x^{-4}y^{-2}z^7}{x^{-3}z^7}=x^{-4-(-3)}y^{-2}z^{7-7}^{} \\ ^{}=x^{-4+3}y^{-2}z^0 \\ ^{}=x^{-1}y^{-2}\cdot1 \\ =x^{-1}y^{-2} \end{gathered}[/tex]
Because any number to the power of 0 is equal to 1. Then, apply the second property to get
[tex]\frac{1}{x^1y^2}=\frac{1}{xy^2}[/tex]
Therefore, the answer is 1/(xy²)
