\(\left(\frac{1}{2}\right)^{t - 1} = 64,\)

rewrite \(64\) as a power of \(\frac{1}{2}\):

\(64 = \left(\frac{1}{2}\right)^{-6}.\)

Equate the exponents: \(t - 1 = -6\)

Thus, \(t = -5\)