Answer
The climber would expend $~~7.8\times 10^6~J~~$ of energy.
Work Step by Step
We can find the change in gravitational potential energy from sea level to the summit of Mount Everest:
$\Delta U = U_f-U_0$
$\Delta U = mgh-0$
$\Delta U = (90~kg)(9.8~m/s^2)(8850~m)$
$\Delta U = 7.8\times 10^6~J$
The climber would expend $~~7.8\times 10^6~J~~$ of energy.
