Question

Please help. I'm stuck.

Answer 1

The root $\sqrt{10}$ can be converted into the power $10^{ \frac{1}{2} }$. Therefore we can rewrite the problem as $(10^{ \frac{1}{2} } )^ {\frac{3}{4} x}$ and then follow the exponent rules about a power to a power, multiplying 1/2 and 3/4 together.

Thus the problem becomes $10^{\frac{3}{8}x}$, which then can be turned into $\sqrt[8]{10} ^{3x}$, making the last option our answer.