Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6 - Page 223: 27

$18$

Using the laws of exponents, the given expression, $ \left( 2^{-1}\cdot3^{-2} \right)^{-1} ,$ is equivalent to \begin{array}{l}\require{cancel} 2^{-1(-1)}\cdot3^{-2(-1)} \\\\= 2^{1}\cdot3^{2} \\\\= 2\cdot9 \\\\= 18 .\end{array}