Practice multiplying and simplifying radical expressions with coefficients and variables.

ⓐ $(6\sqrt{6x^2})(8\sqrt{30x^4})$: Multiply the coefficients and radicands: $(6\sqrt{6x^2})(8\sqrt{30x^4}) = 48\sqrt{180x^6}$ Extract the largest perfect square factor ($36x^6$): $48\sqrt{36x^6 \cdot 5} = 48\sqrt{36x^6} \cdot \sqrt{5}$ Simplify the perfect square and multiply the coefficients: $48 \cdot 6x^3\sqrt{5} = 288x^3\sqrt{5}$

ⓑ $(-4\sqrt[4]{12y^3})(-\sqrt[4]{8y^3})$: Multiply the coefficients ($-4 \cdot -1 = 4$) and radicands: $(-4\sqrt[4]{12y^3})(-\sqrt[4]{8y^3}) = 4\sqrt[4]{96y^6}$ Extract the largest perfect fourth power factor ($16y^4$): $4\sqrt[4]{16y^4 \cdot 6y^2} = 4\sqrt[4]{16y^4} \cdot \sqrt[4]{6y^2}$ Simplify and multiply: $4 \cdot 2y\sqrt[4]{6y^2} = 8y\sqrt[4]{6y^2}$