The root [tex] \sqrt{10} [/tex] can be converted into the power [tex]10^{ \frac{1}{2} } [/tex]. Therefore we can rewrite the problem as [tex](10^{ \frac{1}{2} } )^ {\frac{3}{4} x} [/tex] and then follow the exponent rules about a power to a power, multiplying 1/2 and 3/4 together.
Thus the problem becomes [tex]10^{\frac{3}{8}x}[/tex], which then can be turned into [tex] \sqrt[8]{10} ^{3x}[/tex], making the last option our answer.
