Question

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

Answer 1

Answer:

$(x3y^5)^{\frac{4}{3} \\=[(x^{3 \times \frac{4}{3}}y^{5 \times \frac{4}{3}})\\\\=x^4y^{\frac{20}{3}\\=x^4y^{\frac{18}{3}}y^{\frac{2}{3}}\\=x^4y^6\sqrt[3]{y^2}$

Step-by-step explanation:

Answer 2

Rational exponents work as follows:

$a^{\frac{b}{c}}=\sqrt[c]{a^b}$

So, in your case, we have

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