exponents of exponents multiply, so:

`(x^4)^9=x^(36)`

`(3^5)^3=3^(15)`

`(x^6)^3=x^(18)`

So:

`((3x^4)^9)/((3^5x^6)^3) = (3^9x^(36))/(3^(15)x^(18))`

`a^b/a^c=a^(b-c)`, so:

`(3^9)/(3^(15)) = 3^(-6)` or `1/3^6`

`(x^(36))/(x^(18))=x^(18)`

Thus:

`(3^9x^(36))/(3^(15)x^(18)) = x^(18)/3^6 = x^(18)/729`

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.