Chapter 5 - Section 5.7 - Negative Exponents and Scientific Notation - Exercise Set - Page 409: 56

$\dfrac{1}{81x^{20}}$

Using the laws of exponents, the given expression, $ \left( \dfrac{6x^7}{2x^2} \right)^{-4} ,$ simplifies to \begin{array}{l}\require{cancel} \left( (6\div2)x^{7-2} \right)^{-4} \\\\= \left( 3x^{5} \right)^{-4} \\\\= 3^{1(-4)}x^{5(-4)} \\\\= 3^{-4}x^{-20} \\\\= \dfrac{1}{3^{4}x^{20}} \\\\= \dfrac{1}{81x^{20}} .\end{array}