Question

What is the simplest radical form of the expression?


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

A.
`x^(2)y^(3)√(y)`

B.
`x^(3)y^(2)√(xy)`

C.
`xy^(5)\sqrt[3]{xy}`

D.
`xy^(3)\sqrt[3]{xy}`

Answer 1

`\bf (x^2y^8)^{(2)/(3)}\implies \left( x^{2\cdot (2)/(3)}y^{8\cdot (2)/(3)} \right)\implies x^{(4)/(3)}y^{(16)/(3)}\implies x^{(3)/(3)+(1)/(3)}y^{(15)/(3)+(1)/(3)}\implies x^{1+(1)/(3)}y^{5+(1)/(3)} \\\\\\ x^1\cdot x^{(1)/(3)}\cdot y^5\cdot y^{(1)/(3)}\implies x^1\cdot y^5\cdot x^{(1)/(3)}\cdot y^{(1)/(3)}\implies xy^5\sqrt[3]{x}\sqrt[3]{y}\implies xy^5 \sqrt[3]{xy}`