Question

4TH TIME POSTING THIS BROOOOO MY POINTS

Answer 1

Option d)
`xy^5\sqrt[3]{xy}` is correct

The simplest radical form of the given expression is
`xy^5.\sqrt[3]{xy}`

Explanation:

Given expression is
`(x^2y^8)^{(2)/(3)}`

To find the simplest radical form of the given expression:

`(x^2y^8)^{(2)/(3)}=((x^2y^8)^2)^{(1)/(3)}`

`=((x^4)(y^(16)))^{(1)/(3)}`

`=((x^4))^{(1)/(3)}* (y^(16))^{(1)/(3)}`

`=((x^3.x^1))^{(1)/(3)}* (y^(15).y^1)^{(1)/(3)}`

`=((x^3)^{(1)/(3)}* (x^1)^{(1)/(3)}* (y^(15))^{(1)/(3)}* (y^1)^{(1)/(3)}`

`=x* \sqrt[3]{x}* y^5* \sqrt[3]{y}`

`=xy^5.\sqrt[3]{xy}`

Therefore
`(x^2y^8)^{(2)/(3)}=xy^5.\sqrt[3]{xy}`

The simplest radical form is
`xy^5.\sqrt[3]{xy}`

Therefore Option d)
`xy^5\sqrt[3]{xy}` is correct