Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 65

$16x^{4t+4}$

Using laws of exponents, the given expression simplifies to \begin{align*} & \left( \dfrac{2x^{3t}}{x^{2t-1}} \right)^4 \\\\&= \dfrac{2^4x^{3t(4)}}{x^{4(2t-1)}} \\\\&= \dfrac{16x^{12t}}{x^{8t-4}} \\\\&= 16x^{12t-(8t-4)} \\\\&= 16x^{12t-8t+4} \\\\&= 16x^{4t+4} .\end{align*}