Answer
$\sqrt[6]x$
Work Step by Step
Simplify. $\dfrac{\sqrt[3]{x^2}}{\sqrt[4]{x^2}}$
As per definition of square root property,we have $(p)^{\frac{m}{n}}=(\sqrt[n] {p})^m$
Thus, the given radical term can be written as:
$\dfrac{\sqrt[3]{x^2}}{\sqrt[4]{x^2}}=\dfrac{x^\frac{2}{3}}{x^\frac{2}{4}}$
Since, the power raised to a same exponent or base gets subtract when they are divide.
or,$=x^{\frac{2}{3}-\frac{1}{2}}$
or, $=x^\frac{4-3}{6}$
or, $=x^\frac{1}{6}$
Formula to convert the expression to radical form as: $a^\frac{x}{n}=\sqrt[n]{a^x}$
Hence, the above exponent in radical form can be written as: $\sqrt[6]x$
