Question

Simplify the cubed root of six over the fourth root of six

Answer 1

Answer:

six raised to the one twelfth power

Step-by-step explanation:

The cubed root of 6/the fourth root of 6 equals (6^1/3)/(6^1/4)

6^((1/3)-(1/4))

6^((4-3)/12)

6^1/12

Answer 2

Answer:

six raised to the one twelfth power

Step-by-step explanation:

The problem ask to simplify this expression:

$\frac{\sqrt[3]{6} }{\sqrt[4]{6} }$

In order to do it, we can consider the following propierties:

$\sqrt[y]{a^x} =a^{\frac{x}{y}}\\ \\a^{-n}=\frac{1}{a^n}\\\\x^y x^z=x^{y+z}$

Using the first propierty, we can rewrite the expression as:

$\frac{6^{\frac{1}{3} } }{6^{\frac{1}{4} } }$

Now, let's use the second propierty:

$6^{\frac{1}{3} } 6^{-\frac{1}{4} }$

Finally, using the third propierty:

$6^{\frac{1}{3} } 6^{-\frac{1}{4} }=6^{\frac{1}{3} - \frac{1}{4} }=6^{\frac{1}{12}}$

Therefore the answer is six raised to the one twelfth power