Chapter 6 Rational Exponents and Radical Functions - 6.2 Apply Properties of Rational Exponents - 6.2 Exercises - Skill Practice - Page 425: 49

${\frac{1}{x^4}}$

Given: $(\sqrt[3] x^2.\sqrt[6] x^4)^{-3}=(x^{\frac{2}{3}}.x^{\frac{2}{3}})^{-3}$ Apply the Product of a Power Property: $x^{\frac{2}{3}}.x^{\frac{2}{3}}=x^{\frac{2}{3}+\frac{2}{3}}=x^{\frac{4}{3}}$ The expression becomes: $(x^{\frac{4}{3}})^{-3}=x^{\frac{4}{3}\times(-3)}=x^{-4}$ Apply the Negative Exponent Property: $x^{-4}={\frac{1}{x^4}}$ Hence, the expression becomes ${\frac{1}{x^4}}$