Question

What is the simplest radical form of the expression? (x3y5)4/3

Answer 1

`(x3y^5)^{(4)/(3) \\=[(x^{3  * (4)/(3)}y^{5 * (4)/(3)})\\\\=x^4y^{(20)/(3)\\=x^4y^{(18)/(3)}y^{(2)/(3)}\\=x^4y^6\sqrt[3]{y^2}`

Explanation:

Answer 2

Rational exponents work as follows:

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

So, in your case, we have

`(x^3y^5)^{(4)/(3)} = \sqrt[3]{(x^3y^5)^4}=\sqrt[3]{x^(12)y^(20)}=\sqrt[3]{x^(12)y^(18)\cdot y^2}}=x^4y^6\sqrt[3]{y^2}`