Answer
$\left\{\dfrac{9}{2}\right\}$
Work Step by Step
Raise each side to the power $3$.
$\left(\sqrt[3]{2t-1}\right)^3=2^3$
$2t-1=8$
Add $1$ to both sides.
$\begin{align*}
2t-1+1&=8+1\\
2t&=9\end{align*}$
Divide both sides by $2$.
$\begin{align*}
\dfrac{2t}{2}&=\dfrac{9}{2}\\
t&=\dfrac{9}{2}
\end{align*}$
Hence, the solution set is $\left\{\frac{9}{2}\right\}$.
