Chapter 9 - Roots and Radicals - Chapters 1-9 Cumulative Review Problem Set - Page 432: 3

$144$

The given expression, $ \left( \dfrac{1}{3}-\dfrac{1}{4} \right)^{-2} ,$ simplifies to \begin{array}{l}\require{cancel} \left( \dfrac{4}{12}-\dfrac{3}{12} \right)^{-2} \\\\= \left( \dfrac{1}{12} \right)^{-2} \\\\= \dfrac{1^{-2}}{12^{-2}} \\\\= \dfrac{12^{2}}{1^{2}} \\\\= 144 .\end{array}