Question

what is the expression in radical form?
(4x^3y^2)^(3/10)
enter your answer, in simplest form, in the box.

Explanation:

Step1: Apply power - of - a - product rule

$(4x^{3}y^{2})^{\frac{1}{10}}=4^{\frac{1}{10}}x^{\frac{3}{10}}y^{\frac{2}{10}}$

Step2: Simplify the exponents

$4^{\frac{1}{10}}x^{\frac{3}{10}}y^{\frac{1}{5}}$

Step3: Convert to radical form

$4^{\frac{1}{10}}=\sqrt[10]{4}$, $x^{\frac{3}{10}}=\sqrt[10]{x^{3}}$, $y^{\frac{1}{5}}=\sqrt[5]{y}$
So the expression is $\sqrt[10]{4x^{3}y^{2}}$

Answer:

$\sqrt[10]{4x^{3}y^{2}}$