For this case we have the following expression:
[tex] \sqrt{10}^{\frac{3}{4}x} [/tex]
By power properties, we can rewrite the square root as number 10 as a base and number 1/2 as an exponent.
We have then:
[tex](10^{\frac{1}{2}})^{\frac{3}{4}x}[/tex]
Then, Rewriting we have:
[tex]10^{ \frac{1}{2}\frac{3}{4}x}[/tex]
[tex]10^{\frac{3}{8}x}[/tex]
finally by properties of radicals we have:
[tex] \sqrt[8]{10}^{3x} [/tex]
Answer:
[tex] \sqrt[8]{10}^{3x} [/tex]
option 4
