Answer: Third option
Step-by-step explanation:
Remember that:
[tex]\sqrt[n]{x^n}=x[/tex]
And the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
The expression is:
[tex]\sqrt[4]{\frac{3}{2x}}[/tex]
To simplify this expression, you need to multiply the denominator and the numerator by [tex]2^3x^3[/tex]. Then:
[tex]\frac{\sqrt[4]{3}}{\sqrt[4]{2x}}=\frac{\sqrt[4]{3(2^3x^3)}}{\sqrt[4]{2x(2^3x^3)}}[/tex]
Simplifiying, you get:
[tex]\frac{\sqrt[4]{3(8x^3)}}{\sqrt[4]{2x(2^3x^3)}}=\frac{\sqrt[4]{24x^3}}{\sqrt[4]{2^4x^4}}=\frac{\sqrt[4]{24x^3}}{2x}[/tex]
