Question

What is the simplest radical form of the expression?
(8x^7y^4)^2/3

Answer 1

`4x^4y^2\sqrt[3]{x^2y^2}`

Explanation:

Recall that
`a^{((b)/(c))}=\sqrt[c]{a^b}`.

Therefore, we have:

`(8x^7y^4)^{(2)/(3)}=\sqrt[3]{(8x^7y^4)^2}`

Use the exponent property
`(a^b)^c=a^((b\cdot c))` to simplify:

`(8x^7y^4)^{(2)/(3)}=\sqrt[3]{(8x^7y^4)^2}=\sqrt[3]{64x^(14)y^8}=\boxed{4x^4y^2\sqrt[3]{x^2y^2}}`