Answer
$3x^2y^2 \sqrt[3]{2x^2}$
Work Step by Step
Simplify . $\sqrt[3]{54x^8y^6}$
As per the product rule, we have $\sqrt[n] {pq}=\sqrt[n] {p}\sqrt[n] {q}$
$\sqrt[3]{54x^8y^6}=\sqrt[3] {54}\sqrt[3] {x^8}\sqrt[3] {y^6}$
Thus,
$=\sqrt[3] {3^3}\sqrt[3] {(x^2)^6}\sqrt[3] {(y^2)^3} \sqrt[3]{2x^2}$
or, $=\sqrt[3]{(3x^2y^2)^3} \sqrt[3]{2x^2}$
Hence, the above exponent in radical form can be written as: or, $3x^2y^2 \sqrt[3]{2x^2}$
