Answer
$i$
Work Step by Step
Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
i^{37}
\\\\=
i^{36}\cdot i
.\end{array}
Using the Power Rule of the laws of exponents which is given by $\left( x^m \right)^p=x^{mp},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
i^{36}\cdot i
\\\\=
\left( i^{2} \right)^{18}\cdot i
.\end{array}
Using $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\left( i^{2} \right)^{18}\cdot i
\\\\=
\left( -1 \right)^{18}\cdot i
\\\\=
1\cdot i
\\\\=
i
.\end{array}
