Question

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

Answer 1

`(1)/(w^(29))`

Explanation:

The given expression is
`(w^(-7)(w^(-9))^2)/(w^4)`.

Since,
`w^(-7)=(1)/(w^7)`

And
`w^(9)=(1)/(w^9)`

Expression will become,

`(w^(-7)(w^(-9))^2)/(w^4)=((1)/(w^7)((1)/(w^9))^2)/(w^4)`

`=((1)/(w^7* w^(18)))/(w^4)`

`=((1)/(w^((7+18))))/(w^4)`

`=(1)/(w^(25))* (1)/(w^4)`

`=(1)/(w^(25)* w^4)`

`=(1)/(w^(29))`

Therefore, Simplified form of the given expression will be
`(1)/(w^(29))`.