## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$i$
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}