Answer:
[tex]\frac{1}{w^{29}}[/tex]
Step-by-step explanation:
The given expression is [tex]\frac{w^{-7}(w^{-9})^2}{w^4}[/tex].
Since, [tex]w^{-7}=\frac{1}{w^7}[/tex]
And [tex]w^{9}=\frac{1}{w^9}[/tex]
Expression will become,
[tex]\frac{w^{-7}(w^{-9})^2}{w^4}=\frac{\frac{1}{w^7}(\frac{1}{w^9})^2}{w^4}[/tex]
[tex]=\frac{\frac{1}{w^7\times w^{18}}}{w^4}[/tex]
[tex]=\frac{\frac{1}{w^{(7+18)}}}{w^4}[/tex]
[tex]=\frac{1}{w^{25}}\times \frac{1}{w^4}[/tex]
[tex]=\frac{1}{w^{25}\times w^4}[/tex]
[tex]=\frac{1}{w^{29}}[/tex]
Therefore, Simplified form of the given expression will be [tex]\frac{1}{w^{29}}[/tex].
