Answer
$x=-1$
Work Step by Step
Using the laws of exponents, the given equation, $
8^{x-1}=\dfrac{1}{64}
,$ is equivalent to
\begin{array}{l}\require{cancel}
8^{x-1}=\dfrac{1}{8^2}
\\\\
8^{x-1}=8^{-2}
.\end{array}
Since the bases on both sides are the same, then the exponents can be equated. Hence, the solution to the given equation is
\begin{array}{l}\require{cancel}
x-1=-2
\\\\
x=-2+1
\\\\
x=-1
.\end{array}
