Question

How do I simplify the 6th root of 4 divided by the 3rd root of 4?

Answer 1

So remember some exponentional laws

$x^{m/n} = \sqrt[n]{x^m}$

 $\frac{x^n}{x^m}=x^{n-m}$ and

$x^{-n}= \frac{1}{x^{n}}$
so
 
4 to the 6th root=4^(1/6)
4 to the 3rd root=4^(1/3)

so
$\frac{4^{1/6}}{4^{1/3}} =4^{(1/6)-(1/3)}=4^{(1/6)-(2/6)}=4^{-1/3}$
and  $4^{-1/3}= \frac{1}{4^{1/3}}= \frac{1}{ \sqrt[3]{4} }$

the answer is $\frac{1}{ \sqrt[3]{4} }$