Question

simplify the radical expression. $sqrt3{x^{3}y^{12}}$ write your answer in the form a, $sqrt3{b}$, or $asqrt3{b}$, where a and b are constants or expressions in x and y. use at most one radical in your answer, and at most one absolute value symbol in your answer.

Explanation:

Step1: Split radical into factors

$\sqrt[3]{x^3 y^{12}} = \sqrt[3]{x^3} \cdot \sqrt[3]{y^{12}}$

Step2: Simplify each cube root

$\sqrt[3]{x^3} = x$, $\sqrt[3]{y^{12}} = y^{\frac{12}{3}} = y^4$

Step3: Multiply simplified terms

$x \cdot y^4$

Answer:

$xy^4$