Question

Simplify the expression. Write the answer with positive exponents only. Assume the variable represents a nonzero real number.

Answer 1

Answer:

$\frac{1}{w^{29}}$

Step-by-step explanation:

The given expression is $\frac{w^{-7}(w^{-9})^2}{w^4}$.

Since, $w^{-7}=\frac{1}{w^7}$

And $w^{9}=\frac{1}{w^9}$

Expression will become,

$\frac{w^{-7}(w^{-9})^2}{w^4}=\frac{\frac{1}{w^7}(\frac{1}{w^9})^2}{w^4}$

               $=\frac{\frac{1}{w^7\times w^{18}}}{w^4}$

               $=\frac{\frac{1}{w^{(7+18)}}}{w^4}$

               $=\frac{1}{w^{25}}\times \frac{1}{w^4}$

               $=\frac{1}{w^{25}\times w^4}$

               $=\frac{1}{w^{29}}$

Therefore, Simplified form of the given expression will be $\frac{1}{w^{29}}$.