Question

Simplify the square root of four over the cubed root of four. four raised to the five sixths power four raised to the one sixth power four raised to the three halves power four raised to the one third power

Answer 1

Answer:

$(B)4^{1/6}$

Four raised to the one-sixth power

Step-by-step explanation:

We want to simplify:  $\dfrac{\sqrt{4} }{\sqrt[3]{4} }$

First, we apply the fractional law of indices to each term.

$\text{If } a^{1/x}=\sqrt[x]{a}, then:\\\sqrt{4}=4^{1/2}\\\sqrt[3]{4}=4^{1/3}$

We then have:

$\dfrac{\sqrt{4} }{\sqrt[3]{4} }=\dfrac{4^{1/2} }{4^{1/3} }\\ Applying the division law of indices: \dfrac{a^m }{a^n }=a^{m-n}\\\dfrac{4^{1/2} }{4^{1/3} }=4^{1/2-1/3}\\\\=4^{1/6}$

The correct option is B.