Chapter 6 Rational Exponents and Radical Functions - 6.1 Evaluate nth Roots and Use Rational Exponents - 6.1 Exercises - Mixed Review - Page 419: 82

$\frac{y^2}{3}$

Given: $\frac{3x}{x^3y^{2}}.\frac{y^4}{9x^{-2}}=\frac{3}{9}.\frac{x}{x^3.x^{-2}}.\frac{y^4}{y^2}$ Apply the Product of a Power Property: $x^3.x^{-2}=x^{3+(-2)}=x^1$ Apply the Quotient of Powers Property: $\frac{x}{x^1}=x^{1-1}=x^0=1\\\frac{y^4}{y^2}=y^{4-2}=y^2$ Hence, the expression becomes $\frac{1}{3}.1.y^2=\frac{y^2}{3}$