Answer
$-625$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(5i)(125i)
,$ multiply the numerical coefficients and multiply the $i$'s as if it were a literal coefficient. Then use $i^2=-1$.
$\bf{\text{Solution Details:}}$
Multiplying the numerical coefficients and the $i$'s result to
\begin{array}{l}\require{cancel}
(5\cdot125)(i\cdot i)
\\\\=
625i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
625(-1)
\\\\=
-625
.\end{array}
