Question

Simplify: A fraction. The numerator is the fourth root of x cubed. The denominator is the cube root of x squared.

Answer 1

First it would be helpful to remove the radicals found in the numerator and denominator. We can do this by the property $\sqrt[n]{x^m} = x^{\frac{m}{n}}$.

This means that our fraction now becomes:

$\dfrac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}$

Now, we can subtract the exponents of $x$ because of the fact that the numerator and denominator both have a base of $x$:

$x^{\frac{3}{4} - \frac{2}{3}}$

$x^{\frac{1}{12}}$

Our answer is $\boxed{x^{\frac{1}{12}}}$.