Option 2: [tex]4^{\frac{1}{6}}[/tex] is the correct answer.
Step-by-step explanation:
The radical expressions like these are simplified by using fractional exponents
given
[tex]\frac{\sqrt{4}}{\sqrt[3]{4} }[/tex]
Converting radicals into exponents
When there is no base the exponent is 1/2 and as the base is 3, the exponent will be 1/3
So
[tex]=\frac{4^{\frac{1}{2}}}{4^{\frac{1}{3}}}[/tex]
As the bases of numerator and denominator is same, the exponents can be subtracted
[tex]=4^{\frac{1}{2}-\frac{1}{3}}\\=4^{\frac{3-2}{6}}\\=4^{\frac{1}{6}}[/tex]
Hence,
Option 2: [tex]4^{\frac{1}{6}}[/tex] is the correct answer.
Keywords: Exponents, radicals
Learn more about radicals at:
- brainly.com/question/6073431
- brainly.com/question/6075514
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