Question

Hey you YES YOU pls pLs help a fella out with my last problem:)

what is the simplest radical form of the expression?

Answer 1

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

Explanation:

Use properties

`(ab)^n=a^nb^n\\ \\(a^n)^m=a^(nm)\\ \\a^(m+n)=a^m\cdot a^n`

Then

`(x^2y^8)^{(2)/(3)}=(x^2)^{(2)/(3)}\cdot (y^8)^{(2)/(3)}=x^{2\cdot (2)/(3)}\cdot y^{8\cdot (2)/(3)}=x^{(4)/(3)}\cdot y^{(16)/(3)}`

Note that

`x^{(4)/(3)}=x^{1+(1)/(3)}=x^1\cdot x^{(1)/(3)}=x\sqrt[3]{x}\\ \\ y^{(16)/(3)}=y^{5+(1)/(3)}=y^5\cdot y^{(1)/(3)}=y^5\sqrt[3]{y},`

then

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