Answer:
[tex](B)4^{1/6}[/tex]
Four raised to the one-sixth power
Step-by-step explanation:
We want to simplify: [tex]\dfrac{\sqrt{4} }{\sqrt[3]{4} }[/tex]
First, we apply the fractional law of indices to each term.
[tex]\text{If } a^{1/x}=\sqrt[x]{a},$ then:\\\sqrt{4}=4^{1/2}\\\sqrt[3]{4}=4^{1/3}[/tex]
We then have:
[tex]\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}[/tex]
The correct option is B.
