Question

How do you multiply 9th root of 9x squared times 6th root of 27 x raise to 5?

Answer 1

The 27th root of 729x raised to the 5th power.

Explanation:

9th root of 9x squared can be written as
`color(white)("XXX")(9x)^(2/9)=(3^2)^(2/9) * x^(2/9)`
`color(white)("XXXXXX")=3^(4/9) * x^(2/9)`

6th root of 27x raised to 5 can be written as
`color(white)("XXX")(27x)^(5/6)=(3^3)^(5/6) * x^(5/6)`
`color(white)("XXXXXXX")=3^(15/6) * x^(5/6)`
`color(white)("XXXXXXX")=3^(5/2) * x^(5/6)`

`(9x)^(2/9) xx (27x)^(5/6)`

`color(white)("XXX")=3^(4/9) * x^(2/9) xx 3^(5/2) * x^(5/6)`

`color(white)("XXX")=3^(4/9) * 3^(5/2) xx x^(2/9) * x^(5/6)`

`color(white)("XXX")=3^(10/9) * x^(5/27)`

`color(white)("XXX")=3^(30/27) * x^(5/27)`

`color(white)("XXX")=(3^6)^(5/27) * x ^(5/27)`

`color(white)("XXX")=729^ (5/27) * x^(5/27)`

`color(white)("XXX")=(729x)^(5/27)`